Method and system for calibrating a system parameter

ABSTRACT

A method for performing in a positioning, navigation, tracking, frequency-measuring, or timing system is provided. The method comprises: providing first and second estimates of at least one system parameter during a first time period, wherein the at least one system parameter has a true value and/or true evolution over time during the first time period; providing a local signal; receiving, at a receiver, a signal from a remote source; providing a correlation signal by correlating the local signal with the received signal; providing amplitude and/or phase compensation of at least one of the local signal, the received signal and the correlation signal based on each of the first and second estimates so as to provide first and second amplitude-compensated and/or phase-compensated correlation signals corresponding to the first and second estimates of the at least one system parameter during the first time period, and; determining which of the first and second estimates is nearer the true value and/or true evolution over time of the at least one system parameter during the first time period, based on a comparison between the first and second amplitude-compensated and/or phase-compensated correlation signals. A computer readable medium and system are also disclosed.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a bypass continuation of International ApplicationNo. PCT/GB2018/052716, filed on Sep. 25, 2018, which in turn claimspriority to GB Application No. 1715573.0, filed on Sep. 26, 2017. Eachof these applications is incorporated herein by reference in itsentirety.

FIELD

The present invention is directed to a method and system for calibratinga system parameter, and has particular application to positioning,tracking, navigation, frequency-measuring and timing systems.

BACKGROUND

In a standard Global Navigation Satellite System (GNSS) procedure, areceiver receives a signal broadcast from a remote source, such as asatellite, and correlates it with a locally-produced signal in order toprovide a correlation code such that the receiver may synchronise withthe received signal. Examples of such received signals include GPSsignals, which include Gold Codes encoded within the radio transmission,and GLONASS signals.

Noise may be introduced into the received signal, for example via thecommunications channel through which it is received, or phase changes inthe received signal caused by multi-path effects. As the signal to noiseratio of the received signal decreases, it becomes more difficult toperform accurate correlation of the local signal and the receivedsignal.

It is therefore desirable to provide an improved approach forcorrelating a local signal with a received signal.

SUMMARY

In accordance with a first aspect of the invention there is provided amethod for performing in a positioning, navigation, tracking,frequency-measuring, or timing system, comprising: providing first andsecond estimates of at least one system parameter during a first timeperiod, wherein the at least one system parameter has a true valueand/or true evolution over time during the first time period; providinga local signal; receiving, at a receiver, a signal from a remote source;providing a correlation signal by correlating the local signal with thereceived signal; providing amplitude and/or phase compensation of atleast one of the local signal, the received signal and the correlationsignal based on each of the first and second estimates so as to providefirst and second amplitude-compensated and/or phase-compensatedcorrelation signals corresponding to the first and second estimates ofthe at least one system parameter during the first time period, and;determining which of the first and second estimates is nearer the truevalue and/or true evolution over time of the at least one systemparameter during the first time period, based on a comparison betweenthe first and second amplitude-compensated and/or phase-compensatedcorrelation signals.

The inventors have advantageously realised that correlation of the localsignal with the received signal may be optimised while simultaneouslycalibrating one or more parameters of the system. This is achieved byproviding first and second phase-compensated and/oramplitude-compensated correlation signals, comparing the signals andtypically selecting the compensated correlation signal having the highercorrelation or the more-likely evolution over time. The selection thusmade not only provides an improvement in the correlation of the localsignal and the received signal, but also implies that the estimate ofthe system parameter associated with the compensated correlation signalhaving the higher correlation or the more-likely evolution over time isnearer the true value and/or true evolution over time of the systemparameter.

Indeed, conventionally, phase and amplitude changes in the receivedsignal (for example caused by changes in the line-of-sight path betweenthe receiver and the remote source) were viewed as a nuisance thatreduced positioning accuracy. In the present invention, these amplitudeand/or phase changes in the received signal, embodied as an amplitudeand/or phase evolution over the first time period, are usedadvantageously in order to “test” different amplitude and/or phasecompensations based on different estimates of at least one systemparameter in order to determine which estimate is nearer the true valueand/or evolution over time. Examples of system parameters which may betested in this fashion include position, speed, orientation, heading(direction of motion), local-oscillator frequency error, magnetometerbias error, gyroscope drift rate, accelerometer drift rate, and otherparameters such as would occur to one skilled in the art.

It is envisaged that more than two estimates of a system parameter maybe provided and “tested” using associated amplitude and/or phasecompensation. It is also envisaged that two or more system parametersmay be calibrated substantially simultaneously, by providing first andsecond (and possibly further) estimates of each system parameter.

Phase and/or amplitude compensation can be applied to the receivedsignal, the local signal, or a combination thereof before the signalsare correlated. The phase and/or amplitude compensation may also beapplied after correlation. In an advantageous embodiment, thecompensation may be applied partially to two or all three of the localsignal, received signal and correlation signal. For example,compensation corresponding to an estimate of a local-oscillatorfrequency error may be applied to the received signal, whilstsimultaneously applying compensation to the local signal correspondingto an estimate of the receiver velocity.

Particularly advantageously, phase-compensation enables correlationusing much longer coherent integration times (typically one secondduration or greater) than is possible using conventional processing(typically twenty milliseconds or less in the case of GPS). Longcoherent integration times may boost the received signal-to-noise ratioof otherwise very weak signals, allowing the present invention to beused, for example, in conjunction with attenuated GNSS signals indifficult environments (such as indoors or in urban canyons).Furthermore, the increased correlation time results in an increasedresolution in frequency space by which the present invention may betterdiscriminate between different phase compensations, and, by extension,between different estimates of one or more system parameters. Thefrequency resolution is inversely proportional to the coherentintegration time.

A received signal may include any known or unknown pattern oftransmitted information, either digital or analogue, that can be foundwithin a broadcast signal by a cross-correlation process using a localcopy of the same pattern. The received signal may be encoded with achipping code that can be used for ranging. Examples of such receivedsignals include GPS signals, which include Gold Codes encoded within theradio transmission. Another example is the Extended Training Sequencesused in GSM cellular transmissions.

In practice the received signal may be processed as a complex code,including in-phase and quadrature components. The local signal may besimilarly complex. The correlation signal can be used as a measure ofthe correlation between these complex signals.

The first time period is the time period over which correlation isperformed.

Typically, the first and second estimates of the at least one systemparameter are used to provide respective first and second predictions ofthe phase and/or amplitude evolution of the received signal from theremote source during the first time period, and wherein the amplitudeand/or phase compensation is performed based on said first and secondpredictions.

The estimates of the system parameter may be used in combination with amathematical model to provide the respective predictions of the phaseand/or amplitude evolution of the received signal during the first timeperiod. The model is typically pre-selected for each system parameter.Typically a predicted phase evolution during the first time period isderived from a predicted frequency evolution of the received signalduring the first time period. Different estimates of the systemparameter will give rise to different predictions of the phase and/oramplitude evolution of the received signal during the first time period,thereby meaning that the amplitude and/or phase compensation performedis different for different estimates of the at least one systemparameter. By comparing the correlation signals obtained as a result ofthe amplitude and/or phase compensation, the estimate that is nearer thetrue value and/or true evolution with time can be selected.

The method may further comprise the step of providing a third estimateof the at least one system parameter during the first time period,wherein the third estimate is based upon the determination of which ofthe first and second estimates was nearer the true value and/or trueevolution over time of the at least one system parameter during thefirst time period. In this manner an iterative approach may be used inwhich adjustments to the tested estimates are made until the optimumestimate has been reached.

As an example, suppose the system parameter that we wish to calibrate isthe direction-of-motion of the receiver. In this example we will supposethat this is constant (i.e. time-independent) during the first timeperiod, and therefore has a true (although unknown) value. Using themathematical model, a first estimate of the direction-of-motion willprovide a first predicted amplitude and/or phase evolution over thefirst time period, and a second (different) estimate of thedirection-of-motion over the first time period will provide a secondpredicted amplitude and/or phase evolution over the first time period.By performing amplitude and/or phase compensation of at least one of thelocal signal, received signal and correlation signal for each of theestimates, and comparing the resulting compensated correlation codes tosee which has the higher correlation or the more-likely evolution withtime, we can infer which of the two estimates of the direction-of-motionof the receiver was nearer the real value during the first time period.An iterative approach may be used to determine an optimum estimate.

Typically, the amplitude and/or phase compensation is based on aplurality of vectors derived from the first and second predictions ofamplitude and/or phase evolution over the first time period. In thiscontext the vectors are like a column matrix, representing a number ofvalues. The plurality of vectors may be a sequence of phase vectors, orphasors, which are 2D phase vectors indicative of the predictedamplitude and/or phase changes introduced into the received signalduring the first time period. The plurality of vectors may be combinedwith the at least one of the local signal, the received signal and thecorrelation signal in order to provide the amplitude and/or phasecompensation. In some instances where there is no amplitude evolutionduring the first time period the vectors may be unit vectors.

In particularly advantageous embodiments of the invention, the methodfurther comprises the step of providing a measured or assumed movementof the receiver during the first time period, and wherein the amplitudeand/or phase compensation is based on the measured or assumed movementof the receiver. Typically the first and second estimates of the atleast one system parameter are based on the measured or assumedmovement.

Where the first and second estimates are based on a measured movement ofthe receiver, this is typically provided by at least one sensorconfigured to make measurements from which position and/or orientationand/or movement may be determined. This may be an inertial measurementunit such as an accelerometer, gyroscope, barometer or magnetometer forexample. Other sensors as would be understood by those skilled in theart may be used. The at least one sensor is typically mounted on thereceiver.

Preferably, measurements from the at least one sensor are obtainedduring the first time period to provide a measured movement of thereceiver during the first time period, and this measured movementsubsequently used to predict an amplitude and/or phase evolution of thereceived signal during the time period, using at least one of the systemparameters. The at least one system parameter may be a parameter of amotion and/or position and/or orientation of the receiver during thefirst time period. This may be, for example, a velocity of the receiver,obtained by an analysis of the measurements taken by an accelerometerduring the first time period using an appropriate physical model forconverting the accelerometer measurements into a receiver velocity.First and second estimates of the receiver velocity may then be “tested”using the method of the present invention in order to both optimise thecorrelation over the first time period, and determine which of theestimates of receiver velocity is nearer the true value and/or evolutionover time. The amplitude and/or phase compensation is performed on atleast one of the local signal and received signal that were obtainedduring the first time period. As has been explained above, the amplitudeand/or phase compensation may also be applied to the correlation signal,after correlation.

Other examples of system parameters that are parameters of a motionand/or position and/or orientation of the receiver include a receiverposition, a receiver orientation, a receiver heading, a receiver headingoffset (e.g. offset between the receiver orientation and direction ofmotion), a step length of a user of the receiver (for example for adead-reckoning system), and a line-of-sight vector between the receiverand the remote source. In some instances, the parameter may be the angleof arrival of a reflected or refracted signal originating from a remotesource. For example, such a signal may have been reflected off asurface, or refracted through an inhomogeneous plasma, located betweenthe remote source and the receiver.

The system parameter may be a bias and/or drift rate of at least onesensor. This is particularly advantageous when the at least one sensoris a low-cost sensor (for example as seen in smart phones) which aretypically of low quality and have large inherent biases. For example,first and second estimates of an accelerometer bias may be provided, andamplitude and/or phase compensation performed based on the first andsecond estimates in order to determine which estimate is closer to thetrue value and/or evolution with time of the sensor bias.

The system parameter may be a frequency reference error of the receiveror remote source.

The system parameter may be fixed (i.e. has a constant value) during thefirst time period, or may be time-dependent.

Particularly advantageously, the first and second amplitude-compensatedand/or phase-compensated correlation signals may be fully consistentwith the physical model used for deriving the system parameters frommeasurements obtained by the motion sensors during the first time period(which is the time period over which correlation is performed). This isin contrast to state-of-the-art methods that use piece-wise analysis offrequency and time over the correlation time period which might easilylead to an amplitude and/or phase evolution that is inconsistent with aphysical model of the receiver motion during the time period. Such aninconsistency would be particularly obvious in cases involving a strongreflected signal (that incorporates a change in phase of the receivedsignal), on to which state-of-the-art methods would lock in preferenceto a weaker, but more desired, line of sight signal.

Indeed, as well as allowing calibration of at least one systemparameter, the use of such a measured or assumed movement of thereceiver during the first time period beneficially allows for anincrease in positioning, navigation and/or timing accuracy. If phaseand/or amplitude compensation is provided in a first direction thatextends between the receiver and remote source, it is possible toachieve preferential gains for signals received along this direction.Thus, a line-of-sight signal between the receiver and remote source willgain preferentially over a reflected signal that is received in adifferent direction. In a GNSS receiver this can lead to a remarkableincrease in positioning accuracy because non-line-of-sight signals (e.g.reflected signals) are sufficiently suppressed. The highest correlationmay be achieved for a line-of-sight signal, even if the absolute powerof this signal is less than that of a non-line-of-sight signal. If thesystem parameter is chosen to be a line-of-sight vector between thereceiver and the remote source, then further accuracy can be obtained bytesting different estimates of the true line-of-sight vector, as well assimultaneously calibrating this system parameter.

Amplitude and/or phase compensation based on a measured or assumedmovement of the receiver in the first direction may be referred to as“motion compensation”. Typically vectors indicative of the measured orassumed movement may be used to perform the motion compensation. Thus,motion compensation may be provided of at least one of the local signal,received signal and correlation signal based on each of the first andsecond estimates of at least one system parameter during the first timeperiod.

An assumed movement of the receiver during the first time period may beprovided when there is no sensor present or when the outputs from the atleast one sensor are not available. An assumed movement may becalculated based on patterns of movement in previous epochs.

As has been outlined above, a typical comparison between the first andsecond phase-compensated and/or amplitude-compensated correlationsignals comprises selecting the compensated correlation signal havingthe higher correlation or the more-likely evolution over time. Theresolution in frequency space by which the present invention maydiscriminate between different phase compensations is inverselyproportional to the coherent integration time of the correlation.Therefore, the selected correlation signal may be constrained to liewithin a frequency window of width that is inversely proportional to thecoherent integration time. The coherent integration time may be greaterthan or equal to one second, which is significantly greater than thecoherent integration time used in current state-of-the-art GNSS receiverimplementations (typically twenty milliseconds or less).

The enhanced frequency resolution of the present invention correspondsto an increased resolution of the system parameter values under test. Inan embodiment, a lower bound on a difference between the first andsecond parameter estimates may be chosen to be inversely proportional tothe coherent integration time. In this way, the system may test morefinely separated parameter estimates than is possible using conventionalreceivers, and optimally choose the resolution of the parameterestimates to be tested, avoiding unnecessary computation.

Consider the following worked example: in determining a heading errorone may conduct the following process. Construct a series of amplitudeand/or phase compensated phasors corresponding to a measured or assumedmotion of the receiver (for example detected by a sensor of a motionmodule) along the current heading estimate. Such phase and/or amplitudecompensated phasors may be referred to as “motion compensated phasors”.Construct a second set of motion compensated phasors tailored for asmall change in the heading estimate, e.g. a rotation in heading of Xdegrees. The resolvable difference in estimates is dictated by the speedof the user and the length of the coherent integration time. The Dopplershift of the signal caused by the user motion causes a frequency shiftaccording to the well-known Doppler equation. The resolution of thefrequency measurements that can be made is determined by the inverse ofthe coherent integration time. For example, it is possible using a 1second coherent integration to resolve a Doppler shift of 1 Hz caused byuser motion. These two sets of motion compensated phasors are correlatedwith the incoming data and the correlation signals are compared. If thecurrent heading estimate is closer to the true value than the “test” Xdegree estimate, then its correlation signal will be stronger (highercorrelation). In this way the true heading estimate can be convergedupon through multiple “hypothesis testing” and an optimisation routine.

Such a test using conventional GNSS processing would encounter problems:the correlation signals suffer multipath fading (an effect mitigated bythe phase and/or amplitude compensation of the present invention), whichwould dominate the tests and make it impossible to clearly identifysmall errors in the parameters of interest. The results would in effectby very noisy. Similarly, conventional GNSS processing uses much shortercoherent integration times, reducing the frequency resolution availablefor a conventional GNSS processing method to resolve small changes inparameters. The long coherent integrations times enabled by the presentinvention increase the resolution of the frequency and phasemeasurements. In this way, and for both of these reasons, the presentinvention permits parameters to be learned and monitored more accuratelyand more confidently, and in more difficult signal environments, thancan be achieved by a conventional receiver using standardKalman-filter-based methods.

The method may further comprise storing in memory the estimate that isdetermined to be nearer the true value and/or true evolution over timeof the system parameter. The estimate (which takes the form of a valueand/or evolution over time) may be stored based on the determinationduring the first time period. At a second time or time period, thestored estimate may be re-used as appropriate. The second time or timeperiod is typically subsequent to (after) the first time period. Forexample, the estimate may relate to a sensor bias that may be used inorder to provide positioning, navigation, frequency or timing data atthe second time or time period. The calibration of the system parametersmay be carried out at set time intervals, between which the storedestimate may be used. In the case where the method comprises providing ameasured or assumed movement of the receiver during the first timeperiod, the estimate may be re-used when the measured or assumed motionof the receiver at the second time or time period is substantiallysimilar to that during the first time period.

Such re-use of a stored estimate, where appropriate, advantageouslyreduces the computational load, decreasing power consumption and therebyimproving battery life when implementing the method on a user device.

In a preferred arrangement the receiver is a GNSS receiver and theremote source is a GNSS satellite. Positioning and navigation using GNSSpositioning and navigation devices produces a number of difficultiesindoors, where signals are weak, and in so-called “urban canyons”, wherethere can be multipath signals. By allowing for estimates of systemparameters to be tested by comparing associated compensated correlationsignals, the correlation can be optimised whilst at the same timecalibrating one or more system parameters.

The method of the first aspect is typically a computer-implementedmethod. The method is preferably performed in a positioning, navigation,tracking, frequency-measuring, or timing system

In accordance with a second aspect of the invention there is provided acomputer readable medium comprising instructions that when executed by acomputer cause the computer to perform the method of the first aspect.The computer readable medium may be provided at a download server. Thus,the executable instructions may be acquired by the computer by way of asoftware upgrade.

In accordance with a third aspect of the invention there is providedpositioning, navigation, tracking, frequency-measuring, or timingsystem, comprising: a local signal generator, configured to provide alocal signal; a receiver configured to receive a signal from a remotesource; a correlation unit configured to provide a correlation signal bycorrelating the local signal with the received signal, and; a processorconfigured to perform the steps of: providing amplitude and/or phasecompensation of at least one of the local signal, the received signaland the correlation signal based on first and second estimates of atleast one system parameter during a first time period so as to providefirst and second amplitude-compensated and/or phase-compensatedcorrelation signals corresponding to the first and second estimates ofthe at least one system parameter during the first time period, whereinthe at least one system parameter has a true value and/or true evolutionover time during the first time period and; determining which of thefirst and second estimates is nearer the true value and/or trueevolution over time of the at least one system parameter during thefirst time period, based on a comparison between the first and secondamplitude-compensated and/or phase-compensated correlation signals.

The navigation, tracking, frequency-measuring, timing or positioningsystem may be operable to perform at least one of navigation, tracking,frequency-measuring, timing or positioning operations.

Preferred embodiments of the third aspect of the present invention areset out in the appended claims and provide corresponding advantages ashave been outlined above.

The system may further comprise a motion module configured to provide ameasured or assumed movement of the receiver during the first timeperiod, and wherein the amplitude and/or phase compensation is based onthe measured or assumed movement of the receiver. The motion modulepreferably comprises at least one sensor configured to make measurementsfrom which position and/or orientation and/or movement may bedetermined, and is typically an inertial sensor such as anaccelerometer, gyroscope, barometer or magnetometer. Other sensors aswould be understood by those skilled in the art may be used.

The positioning, tracking, navigation, frequency-measuring, or timingsystem may be provided on a single device. Various modules in the systemcould be provided separately so that the system is distributed. Forexample, certain calculations, such as the calculations performed by thecorrelation unit and motion unit may be undertaken by processors in anetwork. Thus, an electronic user device may offload calculations toother processors in a network where appropriate in the interests ofefficiency.

In a preferred arrangement the system includes a GNSS positioningdevice, and the remote source is a GNSS satellite. Such a GNSSpositioning device may be provided in an electronic user device such asa smartphone.

The system may comprise a memory configured to store the estimate thatis determined to be nearer the true value and/or true evolution overtime of the system parameter. The estimate (which may take the form of avalue and/or evolution over time) may be stored based on thedetermination during the first time period. At a second time or timeperiod, the stored estimate may be re-used as appropriate. For example,the estimate may relate to a sensor bias that may be used in order toprovide positioning, tracking, frequency-measuring, navigation or timingdata at the second time or time period. The calibration of the systemparameters may be carried out at set time intervals, between which thestored estimate may be used. In the case where the system comprises amotion module, the estimate may be re-used when the measured or assumedmotion of the receiver at the second time or time period issubstantially similar to that during the first time period.

Such re-use of a stored estimate, where appropriate, advantageouslyreduces the computational load, decreasing power consumption and therebyimproving battery life when the system is implemented on an electronicuser device.

The estimate that is determined to be nearer the true value and/or trueevolution over time may be stored, for example, in local storage locateda user device where the system is provided on a single device.Alternatively or in addition the estimate may be stored remotely from auser device, for example through use of a client-server system.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described with reference to the attacheddrawings, in which:

FIG. 1 illustrates an example of a system for correlating a digitalsignal and a correlation code;

FIG. 2 illustrates an example of the system for correlating a digitalsignal and a correlation code that does not use phase-compensatedcorrelation based on a phase-compensated correlation sequence;

FIG. 3 illustrates an example of a correlation system suitable for usein a processing system of a system for phase-compensated correlation ofa digital signal and a correlation code;

FIG. 4 illustrates an example of a phase-compensated correlator;

FIG. 5 illustrates an example of a long correlation code generator;

FIG. 6 illustrates an example of a long digital signal buffer;

FIG. 7 illustrates an example of a phase-compensated correlator;

FIG. 8 illustrates an example of a phase-compensated correlator;

FIG. 9 illustrates an example of a phase-compensated correlation codegenerator;

FIGS. 10A and 10B illustrate different examples of a receiver-motionmodule for producing a movement signal;

FIG. 11 illustrates an example of a record medium;

FIG. 12A illustrates an example of a controller;

FIG. 12B illustrates an example of a computer program;

FIG. 13 illustrates an example of a chip-set;

FIGS. 14A, 14B, 14C illustrates examples of a system, comprising aremote device and a remote processing system, that have differentdistributions of functions between the remote device and the remoteprocessing system;

FIG. 15 is a schematic diagram showing a positioning system that may beused according to an embodiment of the invention, and;

FIG. 16 is a flow diagram showing steps that can be undertaken in anembodiment of the invention.

DETAILED DESCRIPTION

FIG. 15 is a schematic diagram showing a positioning system that may beused according to an embodiment of the invention. A receiver 2 includesan antenna 4 for receiving radio signals, including GNSS signals.Received signals are correlated in a correlator 6 against a local signalgenerated by a local signal generator 8. The local signal generator 8 isconfigured to generate local copies of known correlation sequences (suchas pseudorandom number (PRN) codes for GNSS satellites), using afrequency reference of a local oscillator (LO) 10.

An inertial measurement unit (IMU) 12 includes sensors that candetermine the motion, position and/or orientation of the receiver 2during a first time period, in particular the motion, position and/ororientation of the antenna 4. The IMU 12 can include accelerometers,gyroscopic sensors and other inertial sensors. A parameter estimationunit 16 receives data from the IMU obtained during the first timeperiod. In this example, the data from the IMU are used to provide firstand second estimates of at least one system parameter during the firsttime period. The at least one system parameter has a true value and/ortrue evolution over time during the first time period. The parameter maybe, for example, a direction-of-motion of the receiver 2 during thefirst time period. In other examples, the parameter may be a frequencyerror of the LO.

Compensation unit 14 receives data from the IMU which are used toprovide a prediction of the phase and/or amplitude evolution of thereceived signal during the first time period based on a measured orassumed motion of the receiver 2 during the first time period.Compensation unit 14 also receives the first and second estimates fromthe parameter estimation unit 16. The compensation unit 14 calculates aset of phasors representing the predicted evolution of the phase and/oramplitude of the received signal during the first time period dependentupon each of the first and second estimates. The phasors are then usedto perform amplitude and/or phase compensation over the first timeperiod for both the first and second parameter estimates. The amplitudeand/or phase compensation may be performed on the local signal, thereceived signal or the correlation signal provided by correlator 6, or acombination thereof.

First and second amplitude and/or phase-compensated correlation signals,corresponding to the first and second parameter estimates respectively,are provided by the correlator 6 to the comparison unit 18. Here, thecomparison unit 18 determines which of the first and second estimates isnearer the true value and/or true evolution over time of the at leastone system parameter during the first time period by comparing the firstand second correlation signals. This is typically performed by selectingthe correlation signal having the higher correlation or the more-likelyevolution over time.

The determined estimate of the system parameter may then be stored inlocal storage 20. In embodiments, an iterative process may be performedby using the determined estimate to provide a further estimate of theparameter value and/or evolution with time during the first time period,in order to provide an optimal estimate of the system parameter duringthe first time period.

FIG. 16 is a flow diagram showing steps that can be undertaken in anembodiment of the invention, with reference to the receiver 2 forexample.

At step 101, the antenna 4 receives a radio signal, including GNSSsignals, during a first time period. At step 102, IMU data is obtained,by the inertial measurement unit 12, during the first time period.

At step 103, the parameter estimation unit 16 provides first and secondestimates of at least one system parameter having a true value and/orevolution with time during the first time period. The first and secondestimates may be based on the IMU data. Based on the first and secondestimates, together with the data from the IMU, the compensation unit 14provides respective first and second predictions of the phase and/oramplitude evolution of the received signal during the first time period.

At step 104, the signal received during the first time period isprocessed in order to provide phase and/or amplitude compensation. Thisis performed on at least one of the local signal produced by localsignal generator 8, the received signal, and the correlation signalgenerated by correlator 6. The amplitude and/or phase compensation isperformed based on the first and second predictions of the phase and/oramplitude evolution of the received signal during the first time period,and is typically based on a set of phasors representing the predictedamplitude and/or phase evolution. The resulting correlation signals maybe referred to as compensated correlation signals.

At step 105, the comparison unit 18 determines which of the first andsecond parameter estimates is nearer the true value and/or trueevolution over time during the first time period based on a comparisonbetween the first and second compensated correlation signals. Typically,the compensated correlation signal having the highest correlation and/ormost likely evolution over time is selected, and the parameter estimatecorresponding to the selected compensated correlation signal isdetermined to be nearer the true value and/or true evolution with timeduring the first time period.

The estimate that is determined to be nearer the true value and/orevolution over time may then be used to iteratively provide furtherestimates until an optimum value and/or evolution with time isdetermined.

One form of noise that can arise in a communications channel arises frommulti-path effects. A signal received at a receiver may have arrived atthe receiver via multiple different paths each of which has differentcharacteristics such as path length. The multi-path signals received aretherefore generally received at different times and possibly withdifferent attenuation characteristics and phase. Each multi-path signalmay therefore act as noise in relation to each of the other multi-pathsignals. This can be a significant problem in circumstances wheremulti-path conditions are prevalent.

Even where multi-path conditions are not prevalent, noise can arise fromother sources such as for example frequency reference drift due tofrequency reference instability at a receiver, movement of the receivercausing Doppler shifts in frequency, and timing misalignment between atransmitter and the receiver, electromagnetic interference, andintentional jamming.

The signal may also be attenuated by the environment, for exampleobstructions in the propagation channel, degrading the signal to noiseratio of the received signal.

The inventors have realized that by performing a phase-compensatedcorrelation it is possible to significantly improve the correlation ofthe received digital signal and a correlation code. By compensating forphase variations (arising from movement of the receiver and otherwise)the gain of signals received is enhanced and the signal to noise ratioof the received signals is increased.

By, for example, performing phase-compensated correlation along aparticular direction the correlation between received digital signalsand the correlation code is significantly biased towards the correlationof a digital signal received along that particular direction and thecorrelation code. By compensating for phase variations (arising frommovement of the receiver and otherwise) in a particular direction thegain of signals received from that particular direction is enhancedwhile the gain of signals received not from that direction (i.e.reflected signals arriving at the receiver from other directions) isdecreased.

Motion-compensated correlation is a type of phase-compensatedcorrelation that reduces or removes the effects of Doppler frequencyshift arising from movement of a receiver.

The inventors have created new types of phase-compensated correlationsequences.

These phase-compensated correlation sequences may be stored and may bere-used.

One type (a supercorrelator) is a motion-compensated correlationsequence that can be used to perform motion-compensated correlation, forexample, in situations where other error sources such as localoscillator drift are negligible or removed through modelling/estimation.Another type (an ultracorrelator) is a motion-compensated correlationsequence where the local oscillator frequency error is being directlycompensated, without relying on modelling, and can be used to performmotion-compensated correlation.

A further advantage of using phase-compensated correlation is thatlonger correlation periods can be used to improve correlation gain. Theuse of longer correlation periods significantly improves the correlationgain and so makes the receiver significantly more sensitive.

A further advantage of phase-compensated correlation is the ability toperform long coherent integrations.

The following definitions will be used in this detailed description:

A digital signal is a sequence of discrete symbols. A digital signalmay, for example, be a modulated analog carrier wave, a sampled versionof a modulated analog carrier wave or a sampled and quantised version ofa modulated analog carrier wave.

A symbol represents an integer number of one or more bits. A symbol may,for example, be represented by a particular waveform, a sample orsamples of a particular waveform or a quantised sample or samples of aparticular waveform. A sample may, for example, be a complex value or areal value.

A correlation code is a certain sequence of symbols that is known tohave specific autocorrelation properties.

A correlation sequence is a sequence of symbols that is correlated witha digital signal during correlation. The correlation sequence may berepresented in the form of a sequence of real numbers, or a sequence ofcomplex numbers.

Phase-compensated correlation is correlation that uses aphase-compensated correlation sequence.

A phase-compensated correlation sequence is a correlation sequence thathas been phase-compensated, in some examples differently along itslength, in dependence upon a time varying or time invariant phase.

Motion-compensated correlation is correlation that uses amotion-compensated correlation sequence.

A motion-compensated correlation sequence is a correlation sequence thathas been phase-compensated in dependence upon movement (assumed ormeasured) of a receiver. A motion-compensated correlation sequence isused in this document to refer to either a motion-compensated phasorsequence or a motion-compensated correlation code. In practice, themotion compensated correlation sequence is constructed using amotion-compensated phasor sequence.

A motion-compensated phasor sequence is a sequence of phasors that havebeen phase-compensated in dependence upon movement (assumed or measured)of a receiver.

A motion-compensated correlation code is a correlation code that hasbeen compensated by a sequence of phasors that have beenphase-compensated in dependence upon movement (assumed or measured) of areceiver. A motion-compensated correlation code may, for example, beformed by the combination of a correlation code and a motion-compensatedphasor sequence.

Phase compensation can be provided by direct measurements,modelling/predicting/estimating behaviour, or through indirect methodssuch as an optimisation process over a range of possibilities.

A phase-compensated correlation code is a correlation code that has beencompensated by a sequence of phasors that have been phase-compensated independence upon movement (assumed or measured) of a receiver and/orother sources of frequency variation, such as the time-dependentfrequency error on a local frequency reference in a radio receiver. Aphase-compensated correlation code may, for example, be formed by thecombination of a correlation code and a phase-compensated phasorsequence.

Coherent integration is the summation of sequences of symbols in such amanner as to preserve the phase relationship of the input sequencethroughout, such that sections of the sequence can be added togetherconstructively in both amplitude and phase.

FIG. 1 illustrates an example of a system 100 for correlating a digitalsignal 222 and a correlation code 341. The system 100 comprises areceiver system (receiver) 200 and processing system 250.

The receiver 200 comprises an antenna or antennas 202 for receivingsignals 201 to produce an analogue signal 212 comprising a digitalsignal 222. In this example, but not necessarily all examples, theanalogue signal 212 is amplified by a pre-amplifier 204, however thisstage is optional. Next the analogue signal 212, in this example but notnecessarily all examples, is down-converted by down-converter 210 to alower frequency analogue signal comprising a digital signal 222 However,this stage is also optional. The analogue signal 212 is then convertedfrom analogue form to digital form by analogue to digital converter 220to produce a digital signal 222 in digital form. The received digitalsignal 222 is provided, whether in analog form or digital form, toprocessing system 250.

The processing system 250 comprises a correlation system 252 and also,in this example but not necessarily all examples, comprises a controlsystem 254. The correlation system 252 correlates the received digitalsignal 222 with a correlation code 341. The control system 254, ifpresent, may be used to control the correlation system 252.

FIG. 2 illustrates an example of the processing system 250 forcorrelating a digital signal 222 and a correlation code 341. In thisparticular example, but not necessarily all examples, the digital signal22 has been output from an analogue to digital converter 220 and is indigital form. This example does not use phase-compensated correlationbased on a phase-compensated correlation sequence and is intended todemonstrate the difference between phase-compensated correlation using aphase-compensated correlation sequence and correlation that is notphase-compensated because it does not use a phase-compensatedcorrelation sequence.

Initially a phase-adjustment module 260 adjusts the phase of thereceived digital signal 222. This phase adjustment produces an in-phasedigital signal (I) and a quadrature phase digital signal (Q). Thesecomplex digital signals are provided to a correlation module 262 whichcorrelates the phase-adjusted digital signals with a correlation code341. The results of the correlation module 262 are output from thecorrelation system 252 to the control system 254. The control system 254uses the results of the correlation to provide a closed loop phaseadjustment signal 271 to the phase adjustment module 260 and to providea closed loop code adjustment signal 273 to a code generation module 272used to produce the correlation code 341.

Code-phase alignment may be achieved by adjusting the correlation code341 using the closed loop code adjustment signal 273 which may, forexample, form part of a delay locked loop. Carrier-phase alignment maybe achieved by adjusting the phase of the received digital signal viathe closed loop phase adjustment signal 271 which may be part of a phaselocked loop.

While signal to noise levels are sufficiently high and a lock of theclosed control loops is maintained, the closed control loopsautomatically compensate for Doppler shift arising from relativemovement between the antenna 202 and a source of the received digitalsignals 222. However, “lock” may be absent during an acquisition phase,or lost due to temporary signal loss or due to low signal to noiselevels, for example.

The inventors have developed a new processing system 250, illustrated inFIG. 3 that is suitable for use in a system as illustrated in FIG. 1 .

The new processing system provides improved correlation of the receiveddigital signal 222 and a correlation code 341 by using phase-compensatedcorrelation based upon a phase-compensated correlation sequence.

It should be appreciated that the processing system 250 of FIG. 3 , incontrast to the processing system 250 of FIG. 2 , uses open loop control350 to produce a phase-compensated correlation code 322 used in acorrelator 310 to correlate with the received digital signal 222.

The processing system 250 illustrated in FIG. 3 may, for example, be apermanent replacement to the processing system 250 illustrated in FIG. 2or may be used on a temporary basis as an alternative to the processingsystem 250 illustrated in FIG. 2 .

The open loop control 350 of the processing system 250 in FIG. 3 may bebased upon phase parameter information 361. The phase parameterinformation may be provided, for example, from a model (assumed) or froma sensor (measured). In some but not necessarily all examples, the phaseparameter information is sensor information, for example, an assumed ormeasured movement 361 of the receiver 200 and is not based upon feedback(closing the loop) from the results of any correlation.

The processing system 250 for phase-compensated correlation of areceived digital signal 222 and a correlation code 341 may be used foranumber of different applications. It may, for example, be used for timeand/or frequency synchronization and/or channel estimation and/orchannel separation.

The correlation code 341 used may be application-specific. For example,where the processing system 250 is part of a direct sequence spreadspectrum communication system such as a CDMA mobile telecommunicationsreceiver, the correlation code (chipping code) is a pseudo-random noisecode. For example, if the receiver 200 is a receiver for a globalnavigation satellite system (GNSS) the correlation code is apseudo-random noise code, for example, a Gold code. For example, if thereceiver 200 is a receiver for a communication system, the correlationcode may be a training or pilot symbol sequence such as those used inorthogonal frequency division multiplexing (OFDM), long term evolution(LTE) and digital video broadcasting (DVB) standards.

In some examples, the correlation code 341 may be dependent upon anidentity of a transmitter of the digital signal 222 separating thecommunication channel into different code divided channels via codedivision multiple access.

In some circumstances the digital signal 222 is modulated with data, forexample navigation bits in a GNSS system. However, in other examples thedigital signal 222 is not modulated with data such as, for example, whenit is a training or pilot sequence.

FIG. 3 illustrates an example of a correlation system 252 suitable foruse in a processing system 250 of a system 100 for phase-compensatedcorrelation of a digital signal 222 and a correlation code 341. Thephase-compensated correlation system 252 provides a phase-compensatedcorrelator 300 comprising a correlator 310 and a phase-compensatedcorrelation sequence generator 320.

It should be appreciated that FIG. 3 illustrates an example of aphase-compensated correlation system 252 that performs correlation inthe digital domain post-sampling. This phase-compensated correlationsystem 252 is suitable for use in the processing system 250 illustratedin FIG. 2 . However, different processing systems 250 are possible anddifferent phase-compensated correlation systems 252 are possible. Aphase-compensated correlation system 252 does not necessarily have to besuitable for use in the processing system 250 illustrated in FIG. 2 .Some phase-compensated correlation systems 252 may perform correlationin the analog domain before or after down-conversion. Otherphase-compensated correlation systems 252 may perform correlation in thedigital domain but without analog down-conversion or without full analogdown-conversion and they may, in some examples, use digitaldown-conversion.

A phase parameter module 360 which may or may not form part of thephase-compensated correlator 300 provides phase parameter information361, indicative of time-variable phase parameters, to thephase-compensated correlation sequence generator 320.

For example, in some but not necessarily all examples, a receiver-motionmodule 360 which may or may not form part of the phase-compensatedcorrelator 300 provides a movement signal 361, indicative of movement ofthe receiver 200, to the phase-compensated correlation sequencegenerator 320.

The phase-compensated correlation sequence generator 320 comprises aphase-compensated phasor generator 330 which receives the phaseparameter information 361 and produces a phase-compensated phasorsequence 332.

The phase-compensated correlation sequence generator 320 additionallycomprises a correlation code generator 340 which produces a correlationcode 341.

The phase-compensated correlation sequence generator 320 additionallycomprises a combiner (mixer) 336 which combines the phase-compensatedphasor sequence 332 and the correlation code 341 to produce aphase-compensated correlation code 322.

The phase-compensated correlation code 322 is provided by thephase-compensated correlation sequence generator 320 to the correlator310 which correlates the phase-compensated correlation code 322 with thereceived digital signal 222 to produce the correlation output 312.

The phase-compensated correlator 300 when performing motion-compensationcomprises an open loop 350 from the receiver-motion module 360 throughthe phase-compensated correlation sequence generator 320 to thecorrelator 310. There may be feedback resulting from the correlationoutput 312 to the phase-compensated correlation sequence generator 320.Closed loop feedback can occur between the output of thephase-compensated correlator 300 and the phase-compensated correlationsequence generator 320 or the phase parameter module 360 or the phaseadjust module 260 or the down-convertor 210

It will therefore be appreciated that the correlator 310 performs thefollowing method: correlating a digital signal 222 provided by areceiver 200 with a phase-compensated correlation code 322, wherein thephase-compensated correlation code 322 is a correlation code 341 thathas been compensated at or before correlation using one or more phasors.The correlation code 341 is compensated for phase variation at or beforecorrelation by combining the correlation code 341 with thephase-compensated phasor sequence 332. The phase-compensated phasorsequence 332 is dependent upon phase variation during the time that thereceiver 200 was receiving the digital signal 222.

The use of an open loop 350 for controlling the phase-compensatedcorrelation has advantages, for example, it is fast because the controlis not based upon the result of a preceding correlation. The use of theopen loop control to perform phase-compensated correlation enables thecorrelator 310 to operate in situations where there is a low signal tonoise ratio.

Although in FIG. 3 phase parameter module 360, the phase-compensatedcorrelation sequence generator 320 and the correlator 310 areillustrated as part of the phase-compensated correlator 300, in otherexamples only the correlator 310 may be part of the correlation systemwith the phase-compensated correlation code 322 being provided to thephase-compensated correlator 300 by a phase-compensated correlationsystem generator 320 that is not part of phase-compensated correlator300. In other examples, only the correlator 310 and thephase-compensated correlation sequence generator 320 may be part of thephase-compensated correlator 300 with the phase parameter module 360providing the phase parameter information 361 to the phase-compensatedcorrelator 300.

Although in this example, the phase-compensated correlation sequencegenerator 320 is illustrated as a single entity comprising thephase-compensated phasor generator 330, the correlation code generator340 and the combiner (mixer) 336, it should be understood that these maybe components distinct from the phase-compensated correlation sequencegenerator 320 or combined as components other than those illustratedwithin the phase-compensated correlation sequence generator 320.

It will be appreciated by those skilled in the art that thephase-compensated correlator 300 illustrated in FIG. 3 is a significantand remarkable departure from what has been done before in that itadopts a counter-intuitive approach by modifying the correlation code341 at or before correlation even though those correlation codes 341 mayhave been carefully designed for excellent cross-correlation results.

The phase-compensated correlator 300 illustrated in FIG. 3 may bepermanently functional or may be temporarily functional. For example itmay be functional during a satellite acquisition phase in a GNSSreceiver, and/or when there is signal loss and/or when there are lowsignal to noise levels for example. The phase-compensated correlator 300may preserve the phase coherence of the digital signal 222, thusallowing longer coherent integration times.

FIG. 4 illustrates an example of the phase-compensated correlator 300illustrated in FIG. 3 . This figure illustrates potential sub-componentsof the correlator 310, and the phase-compensated correlation sequencegenerator 320.

In this example the phase-compensated phasor generator 330 produces aphase-compensated phasor sequence 332 that comprises an in-phasecomponent I and a quadrature phase component Q. Both of the in-phasecomponent I and the quadrature phase component Q are mixed 313 with thesame correlation code 341 produced by the code generator 340 to produceas the phase-compensated correlation code 322 an in-phase component Iand a quadrature phase component Q. The correlator 320 mixes 312 thein-phase component of the phase-compensated correlation code 322 withthe received digital signal 222 and performs an integration and dump 314on the result to produce an in-phase correlation result 312. Thecorrelator 310 mixes 312 the quadrature phase phase-compensatedcorrelation code 322 with the same received digital signal 222 andperforms an integration and dump 314 on the result to produce thequadrature phase correlation result 312.

It is important to note that the production of in-phase and quadraturephase signals occurs within the phase-compensated correlation codegenerator 320 when the phase-compensated phasor sequence 332 isproduced. The combination (mixing) of the phase-compensated phasorsequence 332 with the correlation code 341 produces thephase-compensated correlation code 322 which is correlated with thereceived digital signal 222 to produce the correlation output 312.

The integration performed within the correlator 310 produces a positivegain for those received digital signals 222 correlated with thephase-compensated phasor sequence 332. Those received digital signals222 that are not correlated with the phase-compensated phasor sequence332 have a poor correlation with the phase-compensated correlation code322. There is therefore a differential gain applied by thephase-compensated correlator 300 to received digital signals 222compared to noise. It will therefore be appreciated that thephase-compensated correlator 300 significantly improves correlationperformance.

Parametric Model for Phase Variation

A phase sequence {ϕ(t_(n))} is defined by a sequence of N (N>1) phasevalues ϕ(t_(n)) in radians at N defined times t_(n) during a time t=0 tot=T. The time interval t_(n-1) to t_(n) corresponds to the radiosampling interval.

ϕ(t _(n))=∫₀ ^(t) ^(n) 2π·F(t)·dt+ϕ  -Equation 1

or

ϕ(t _(n))=ϕ(t _(n-1))+∫_(t) _(n-1) ^(t) ^(n) 2π·F(t)·dt  -Equation 2

where

F(t)=f_(D)(t)+f_(Rerr)(t) and ϕ₀ is the initial value of phase at timet=0.

F(t) in the integral is time varying on a timescale down to the radiosampling period—that is the time between successive radio samples. It isnot fixed over the correlation code word length but varies along thecorrelation code word length.

f_(D)(t) is the (time dependent) Doppler frequency at the receiver dueto user and source (e.g. a satellite) motion

f_(Rerr)(t)=is the (time dependent) receiver frequency referencefrequency error

Where, from the first order Doppler equation f_(D)=(1+(v_(u)/c))(f_(o)+f_(Serr)(t))

where

c is the speed of light

v_(u) is the (time dependent) relative speed of the receiver towards theactual or assumed signal source in the direction of u(v_(u)=(v_(s)−v_(r))·u).

v_(r) is the (time dependent) velocity of the receiver,

v_(s) is the (time dependent) velocity of the source of the digitalsignal,

u is the (time dependent) unit vector defining a direction of arrival ofa signal, for a directly received signal this defines the line of sight(LOS) unit vector u_(LOS) between receiver and signal source, but it mayalternatively be an expected direction of arrival.

f_(o) is the nominal transmitted frequency. All signal sources may havea common f_(o).

f_(Serr)(t) is the (time dependent) source frequency reference frequencyerror.

It is not normally necessary to use a higher order Doppler equation suchas a relativistic Doppler equation. Although it may be used in somecircumstances e.g. for very long integration times (many seconds).

The phase ϕ(t_(n)) is the total change in phase produced as aconsequence of the nominal transmitted frequency, any Doppler frequencyshift resulting from motion of the receiver relative to the source, andany frequency errors associated with the source and receiver frequencyreferences. It may be referred to as the ‘total’ phase, or as thecompensation phase as it is used to compensate correlation or as a modelphase as it is based on a parametric model where the potentiallyvariable parameters may be for example f_(Rerr)(t), v_(r) v_(s) u,f_(Serr)(t).

ExpandingEquation1 $\begin{matrix}{{\left. {\left. \left. \begin{matrix}{\phi\left( t_{n} \right)} & {= {\int_{0}^{t_{n}}{2{\pi \cdot \left\lbrack \left\{ {1 + \left( \frac{\left. {\left( {{v_{s}(t)} - {v_{r}(t)}} \right) \cdot {u(t)}} \right\rbrack}{c} \right.} \right. \right.}}}}\end{matrix} \right) \right\}\left( {f_{o} + {f_{Serr}(t)}} \right)} \right\rbrack \cdot {dt}} + \phi_{o}} & {{Equation}3}\end{matrix}$

The phase sequence {ϕ(t_(n))} is therefore modelled as dependent uponf_(o), f_(Rerr), f_(Serr), v_(s), v_(r) and u. The phase sequence{ϕ(t_(n))} according to this model can therefore be used to improvephase coincidence/alignment between a correlation sequence and areceived signal during correlation, significantly improving correlationgain. The model is used to produce a phase-compensated correlation codethat represents the digital signal as received according to the model.

It should be noted that the integral in Equation 2 for determining asingle phase value ϕ(t_(n)) is over a time period less than acorrelation code word length. It is therefore possible to account forchanges, for example, in receiver motion on timescales shorter than asingle correlation code word length. It should also be noted that thevalue of F(t) in Equations 1 and 2 may vary on a timescale shorter thana correlation code word length. The time duration T of the phasesequence {ϕ(t_(n))} is in some examples equal to one or more correlationcode word durations. In some examples it may be thousands of correlationcode word lengths.

The phase values within the phase sequence {ϕ(t_(n))} vary at the radiosampling rate. The frequencies f_(Rerr)(t), f_(Serr)(t) might beconstant over more than one radio sample or the receiver may bestationary over more than one radio sample, but the phase is alwayschanging, according to Equations 1-3, it is not constant over thecoherent integration time T.

Equation 3 expressing the total phase variation ϕ(t_(n)) may bere-written as:

ϕ(t _(n))=ϕ_(fo)(t _(n))+ϕ_(f_Serr)(t _(n))+ϕ_(f_Rerr)(t_(n))+ϕ_(Doppler)(t _(n))+ϕ₀  -Equation 4

ϕ_(fo)(t_(n)) is the phase variation due to nominal transmissionfrequency.

ϕ_(fo)(t _(n))=∫₀ ^(t) ^(n) 2π·f _(o) ·dt

ϕ_(f_Serr)(t_(n)) is the phase variation due to satellite frequencyreference frequency error.

ϕ_(f_Serr)(t _(n))=∫₀ ^(t) ^(n) 2π·f _(Serr)(t)·dt

ϕ_(f_Rerr)(t_(n)) is the phase variation due to receiver frequencyreference frequency error.

ϕ_(f_Rerr)(t _(n))=∫₀ ^(t) ^(n) 2π·f _(Rerr)(t)·dt  -Equation 5

As the variation in this phase ϕ_(f_Rerr)(t_(n)) arises from thereceiver frequency reference frequency error, it may be called thereceiver frequency reference phase.

ϕ_(Doppler)(t_(n)) is the phase variation due to Doppler frequencyshift.

$\begin{matrix}{\left. {\left. \begin{matrix}{\phi_{Doppler}\left( t_{n} \right)} & {= {\int_{0}^{t_{n}}{2{\pi \cdot \left\lbrack \left( \frac{\left. {\left( {{v_{s}(t)} - {v_{r}(t)}} \right) \cdot {u(t)}} \right\rbrack}{c} \right. \right.}}}}\end{matrix} \right)\left( {f_{o} + {f_{Serr}(t)}} \right)} \right\rbrack \cdot {dt}} & {{Equation}6}\end{matrix}$

As the variation in this phase ϕ_(Doppler)(t_(n)) arises from theDoppler frequency shift, it may be referred to using the moniker‘Doppler phase’.

In some examples, it may be assumed that ϕ_(fo)(t_(n)) is generated froma fixed frequency and ϕ_(f_Serr)(t_(n)) is known and/or well-behaved andtheir effects on the total phase variation ϕ(t_(n)) and correlation canbe compensated for over the coherent integration time by a constantfrequency component.

Using the phase model defined by Equation 4 (or 3), partial knowledge ofthe total phase variation ϕ(t_(n)) and the results of correlations withone or more received signals, it may be possible to determine the phasevariation due to receiver frequency reference frequency errorϕ_(f_Rerr)(t_(n)) (if any), and/or the phase variation due to Dopplerfrequency shift ϕ_(Doppler)(t_(n)) (if any) and/or the total phasevariation ϕ(t_(n)).

The phase variation due to receiver frequency reference frequency errorϕ_(f_Rerr)(t_(n)) depends on f_(Rerr)(t_(n)) which may vary over thecoherent integration time, particularly for longer coherent integrationtimes and/or less stable frequency references.

The phase variation due to receiver frequency reference frequency errorϕ_(f_Rerr)(t_(n)) may be used to compensate a less accurate frequencyreference, enabling the use of low cost frequency references at thereceiver.

By measuring the phase variation due to receiver frequency referencefrequency error ϕ_(f_Rerr)(t_(n)) at different times, it may be possibleto model the phase variation due to receiver frequency referencefrequency error ϕ_(f_Rerr)(t_(n)) at other times. For example, apolynomial fit or other model may be applied to the phase variations dueto receiver frequency reference frequency error ϕ_(f_Rerr)(t_(n))determined at different times. It may also be possible to useaccelerometers, gyroscopes, or other motion measurement sensors todetermine the forces on the receiver frequency reference that result inpredictable frequency changes. In this way, frequency reference errorsdue to forces from motion can be directly compensated in theconstruction or modelling of this frequency reference error phasor term.

The phase variation due to Doppler frequency shift. ϕ_(Doppler)(t_(n))depends on f_(Doppler)(t) which may vary over the coherent integrationtime, particularly for longer coherent integration times and/or a movingreceiver.

The phase variation due to Doppler frequency shift ϕ_(Doppler)(t_(n))may be used to calibrate any assumptions or measurements concerningv_(r), v_(s), u.

A knowledge of the phase variation due to the Doppler frequency shiftϕ_(Doppler)(t_(n)) allows that variation to be compensated for duringcorrelation. This compensation is particular to v_(r), v₅ u defining thephase variation due to the Doppler frequency shift—it is therefore aselective filter dependent on v_(that) significantly attenuates signalsfrom incorrect sources (v_(s)) and from incorrect directions of arrival(u). A moving receiver may therefore have significantly increased gainfor ‘correct’ signals and reduced gain for ‘incorrect’ signals arisingfrom the motion-compensated correlation provided by the phase variationdue to the Doppler frequency shift ϕ_(Doppler)(t_(n)).

A knowledge of the time variation of the total phase variation ϕ(t_(n))allows that variation to be compensated for during correlation enablingextremely long coherent integration times and very significantlyincreased gain.

In some but not necessarily all examples, it may be assumed that thephase variation due to the receiver frequency reference frequency errorϕ_(f_Rerr)(t_(n)) (and also ϕ_(f_Serr)(t_(n))) is known and well behavedover the coherent integration time used for correlation. The remainingunknown component of the total phase variation ϕ(t_(n)) is the phasevariation due to Doppler frequency shift ϕ_(Doppler)(t_(n)) and this maybe calculated based on v_(r), v_(s), u. The value of v_(r) may beassumed or measured. The coherent integration time may be manycorrelation code words in length, for example, a length of 1000correlation code words of duration 1 ms is possible.

In some but not necessarily all examples, the phase variation due to thereceiver frequency reference frequency error ϕ_(f_Rerr)(t_(n)) over thecoherent integration time used for correlation is directly measured. Ifϕ_(f_Serr)(t_(n)) is known, the remaining unknown component of the totalphase variation ϕ(t_(n)) is the phase variation due to Doppler frequencyshift ϕ_(Doppler)(t_(n)) and this may be calculated based on v_(r),v_(s), u. The value of v_(may) be assumed or measured. The coherentintegration time may be many correlation code words in length, forexample, a length of 10000 correlation code words of duration 1 ms ispossible.

In some but not necessarily all examples, it may be assumed thatϕ_(Doppler)(t_(n)) is known and well behaved over the coherentintegration time used for correlation. This may, for example, be assumedwhen a satellite signal source is directly overhead or v_(r), v_(s), uare known. The remaining unknown component of the total phase variationϕ(t_(n)) is the phase variation due to the receiver frequency referencefrequency error ϕ_(f_Rerr)(t_(n)) and the phase variation due tosatellite frequency reference frequency error ϕ_(f_Serr)(t_(n)) (if any)and this component may be found by direct measurement using correlationof a high quality received signal or using hypothesis testing using oneor more lower quality signals.

In some but not necessarily all examples, it may be assumed that thephase variation due to the receiver frequency reference frequency errorϕ_(f_Rerr)(t_(n)) is known to be within certain bounds, defined forexample by an expected stability (e.g. Allan variance) of the receiverfrequency reference, and/or the phase variation due to the Dopplerfrequency shift ϕ_(Doppler)(t_(n)) is known to be within certain bounds,defined for example by an expected stability of inertial sensors used tomeasure v_(r), and/or expected values of v_(r) Multi-signal hypothesistesting may be used to determine the actual phase variation over thecoherent integration time due to receiver frequency reference frequencyerror ϕ_(f_Rerr)(t_(n)) and/or the actual phase variation due to Dopplerfrequency shift ϕ_(Doppler)(t_(n)) The hypothesises are constrained bythe phase model (Equation 3, 4) and the expected bounds.

It may, for example, be assumed that the phase variation due to thereceiver frequency reference frequency error ϕ_(f_Rerr)(t_(n)) is knownto be within certain bounds, when a model for estimating the phasevariation due to the receiver frequency reference frequency errorϕ_(f_Rerr)(t_(n)) has expired and needs to be renewed.

It may, for example, be assumed that the phase variation due to theDoppler frequency shift ϕ_(Doppler)(t_(n)) is known to be within certainbounds, when it is determined that a receiver has moved indoors or allreceived signals are simultaneously attenuated.

It will be appreciated that when certain phase parameters in Equation 3are zero or known (e.g. from direct measurement, signal source selectionor otherwise) then it may be possible to determine other unknown phaseparameters, and their evolution in time, using the model of Equation 3.It may for example be possible to determine v_(r)(t), for example, usinghypothesis testing described below.

It will be appreciated that the Doppler phase ϕ_(Doppler)(t_(n)) isdependent upon, inter alia, (in increasing specificity) movement of thereceiver v_(r); the movement of the receiver relative to the signalsource (v_(s)−v_(r)); the component (v_(u)=(v_(s)−v_(r))·u) of thevelocity of the receiver relative to the signal source along a defineddirection u.

Phase Parameters

In order to refer to parameters coherently within this document, it isuseful to classify the parameters that affect the total phase ϕ(t_(n))as phase parameters. These phase parameters may be referred tocollectively as phase parameters p(t) or individually as a phaseparameter p_(i)(t) where the index i indicates a type or class ofparameter. The phase parameters p(t) may vary continuously with time,and are defined at each time t_(n) where the time interval t_(n-1) tot_(n) corresponds to the radio sampling interval.

A receiver system parameter is a phase parameter p_(i)(t) that affectsthe phase of all received signals to the same extent.

The types of phase parameters p(t) may be classified as:

f_(Rerr) is an example of a receiver system parameter. It is a parameterthat affects the phase ϕ(t_(n)) of all signals received by the receiverto the same extent. It can be removed by applying the same time-varyingphase sequence {ϕ_(f_Rerr)(t_(n))} to all signals.

If there is a heading (orientation) error, there is a correspondingerror in v_(r) (Δv_(r)). This heading error is a parameter that affectsthe phase of all signals received by the receiver.

v_(r) and v_(s) are examples of kinematic parameters.

v_(r) is an example of a receiver kinematic parameter, as is its relateddisplacement parameter δr_(r).

v_(s) is an examples of a source kinematic parameter, as is its relateddisplacement parameter δr_(s).

The velocity of any object may be resolved into two parameters heading hand speed s for velocity-over-the-ground v_(r)

u is an example of a direction of signal arrival parameter.

u_(LOS) is a vector aligned along a line of sight and is an example thatis both a vector parameter and a kinematic parameter (a relativedisplacement parameter) as it is defined by r_(s)−r_(r) (r_(s) is adisplacement of the source of the digital signal and r_(r) is adisplacement of the receiver).

The evolution (variation in time) of the phase parameters p(t) over atime period such as a coherent integration time T may be represented bythe multi-valued sequence {p(t_(n))}.

The evolution (variation in time) of a particular phase parameterp_(i)(t) over a time period such as a coherent integration time T may berepresented by the multi-valued sequence {p_(i)(t_(n))}.

One or more of the phase parameters may be provided in phase parameterinformation 361 to produce a phase-compensated phasor sequence 332.

The time-varying phase sequence may be applied before or aftercorrelation. If applied after correlation it is likely to be asubsampled version of one that would be applied before correlation. Inthis case F(t) is approximated by a staircase function where F(t) isconstant during each correlation code word correlation then jumps to thenew value for the next one, and so on.

F(t) therefore varies over the coherent integration time and is based ona parametric model. The model does not dependent upon previouscorrelation results and can therefore be applied before any correlationhas occurred.

Phasor Sequence

The phase sequence {ϕ(t_(n))} represents an evolution (variation overtime) of the phase through the defined times t_(n) during the time t=0to t=T.

A complex phasor X(t_(n)) represents a phase ϕ(t_(n)) at a defined timet_(n)

X(t _(n))=exp(iϕ(t _(n))).  -Equation 7

A phasor sequence {X(t_(n))} comprises multiple phasors X(t_(n)) eachrepresenting a phase ϕ(t_(n)) at a different defined time (Arg(X(t_(n)))=ϕ(t_(n))).

{X(t_(n))} is the sequence of phasors X(t_(n)) for each n where 1≤n≤Nand N≥2.

Each phasor X(t_(n)) represents a phase compensation based upon thephase of the receiver at time t_(n) that is applied to a correspondingsample of the correlation code 341. In this way, the correlation code341 becomes phase-compensated when the correlation code 341 is combinedwith the phase-compensated phasor sequence 332.

A phasor X(t) is a transformation in phase space and it is complexvalued, producing the in-phase component of the phase-compensated phasorsequence 332 via its real value and the quadrature phase component ofthe phase-compensated phasor sequence 332 via its imaginary value. Thephasor X(t) is a cyclic phasor and may be expressed in a number ofdifferent ways, for example as a vector in the complex plane. The anglefrom the real axis to this vector is equal to the phase angle ϕ(t) inradians and is positive valued for counter clockwise rotation. Althoughin this example, the phasor X(t) has a constant amplitude within thephase-compensated phasor sequence 332, in other examples, the phasor mayrepresent both a rotation and a change in amplitude instead of just arotation. However, in other examples, such as the one illustrated, thephasor is for rotation only.

Phase-Compensated Correlation

The complex correlation result R for the time interval T_(g)−T_(g-1) is

R _(g)=∫_(T) _(g-1) ^(T) ^(g) S(t)·[X(t)·C(t)]*dt  -Equation 8

where X(t) is the phasor, S(t) is the digital signal, and thecorrelation code word C(t) can be a single correlation code word or aconcatenation of a base correlation code word for the received signal.

The time interval T_(g)−T_(g-1) (the coherent integration time period)is equal to one or more correlation code durations and can be very long,for example many seconds of data (many thousands of correlation codewords in length). The term-by-term multiplication of X(t). C(t) producesa phase-compensated correlation code that in certain circumstances maybe re-used without recalculation. The asterisk in Equation 8 denotes thecomplex conjugate.

The signal S(t) may be any signal which has properties that allowcorrelation (i.e. have repetitive or predictable signal content, such asGNSS signals, cellular telecommunications signals, DVB-T signals, radarsignals, sonar signals, etc). In some but not necessarily all examples,the signal source is a GNSS satellite.

Correlation may occur pre-acquisition or post-acquisition in a GNSSreceiver. Acquisition refers to determining the code delay and carrierfrequency of a received signal. In some examples, correlation may usethe correlators of the GNSS receiver acquisition engine.

A phase sequence {ϕ(t_(n))} comprises multiple phase values ϕ(t_(n)) fordifferent times within a single correlation code word. A phase sequence{ϕ(t_(n))} represents an end-to-end multi-step directed (not random)path through a phase-time space. It has a sub-code word resolution(multiple different frequency values F(t) per correlation code word).The phase sequence {ϕ(t_(n))} is a known, assumed or modelled end-to-endmulti-step path through a phase-time space and is assessed over itswhole length T which is the time period of correlation (coherentintegration).

It should be noted that the correlation performs coherent integrationalong the vector u. Signals that do not arrive along u do not coherentlyintegrate for different positions of the receiver.

A Priori-Compensation

If the phase parameter sequence {p(t_(n))} for a received signal isknown or assumed over a time period (e.g. T), then the phase sequence{ϕ(t_(n))} is precisely defined for that time period. This means thatvariations in the phase over that time period can be preciselycompensated for reducing phase errors affecting the coherent integration(correlation). This allows the coherent integration time to be verysignificantly extended by using a correlation code word (e.g. aconcatenated correlation code word) for the coherent integration. Thisin turn very significantly increases signal gain. Previously unusablesignals can then be used.

Thus, if a correct phase sequence {ϕ(t_(n))} is used to create a correctphasor sequence {X(t_(n)),} then extremely long coherent integrationtimes of many correlation code word lengths may be used to increasegain.

The sensitivity of the correlation can be increased by increasing thelength of phase sequence {ϕ(t_(n))} and the coherent integration time(T=T_(g)−T_(g-1)) in Equation 8). The sensitivity may be increased untilweak signals can be seen above noise.

The most significant effects on the phase sequence {ϕ(t_(n))} during thecoherent integration time T typically arises from instabilities in thereceiver frequency reference (phase parameter f_(Rerr)) and a change inthe relative position/orientation of the receiver to the signal source(phase parameters u and v_(r)).

The phasor sequence {X(t_(n))} may, in some examples, be amotion-compensated phasor sequence comprising motion-compensated phasorsX(t_(n)) based on a motion-compensated phase sequence {ϕ(t_(n))}. Themotion-compensated phase sequence {ϕ(t_(n))} is based upon an assumed ormeasured motion of the receiver such as, for example, v_(u)(t) orv_(r)(t) or v_(s)(t)−v_(r)(t) or v_(r)(t)·u. The motion-compensatedphasor sequence {X(t_(n))} is based upon the motion-compensated phasesequence {ϕ(t_(n))}. The phase sequence {ϕ(t_(n))} may be furthercompensated for errors and instabilities associated with the frequencyreferences at both the transmitter and receiver, and other sources ofphase error.

Parameter Calibration By Hypothesis Testing

A putative phase sequence {ϕ(t_(n))} can be used to create a putativephasor sequence {X(t_(n))} based on an hypothesis H and the resultantgain of the correlation result R or another assessment can be used todetermine whether the putative phase sequence {ϕ(t_(n))} and phasorsequence {X(t_(n))} is a correct phase sequence {ϕ(t_(n))} and putativephasor sequence {X(t_(n))}. It may be possible, in this way, todetermine corresponding parameter sequences {p(t_(n))} for one or moreof the phase parameters p_(i)(t) that determine {X(t_(n))} and{ϕ(t_(n))} such as frequency f_(Rerr), h, v_(r), u, v_(s), δr_(s),δr_(r) etc.

Parameters may vary on a very short timescale, such as within a phasesequence {ϕ(t_(n))}. The parameters p_(i) may vary continuously withtime, and in some but not necessarily all examples are defined at eachtime t_(n) where the time interval to t_(n) corresponds to the radiosampling interval.

The method may, for example, comprise: causing correlation of multiplesamples of a digital signal received by a receiver during a time period,via a communications channel, and the same correlation code compensatedusing different multiple putative phasor sequences to produce acorrelation result for each different multiple putative phasor sequence,wherein each phasor sequence comprises multiple phasors representingdifferent phases at different defined times during the time period, andthe multiple putative phasor sequences are different in that eachputative phasor sequence is based on a different hypothesis regardingthe evolution of the frequency and phase through the defined timesduring the time period; and

using the correlation results to determine a preferred hypothesisregarding evolution of the frequency and phase during the time period.

Different hypotheses are based on phase parameters of a parametric modelof phase evolution (see Equation 3)

This may be extended to using multiple different phase sequences{ϕ(t_(n))}_(k) based on multiple hypotheses {H_(k)} in parallel. Eachdifferent putative phase sequence {ϕ(t_(n))}k can be used to create aputative phasor sequence {X(t_(n))}_(k) and the resultant gain of thecorrelation result R_(k) or another assessment can be used to determinewhich of the multiple putative phase sequence {ϕ(t_(n))}_(k) (and phasorsequences {X(t_(n))}_(k)) is a correct or, at least, a best phasesequence {ϕ(t_(n))}_(#)(and putative phasor sequence {X(t_(n))}_(#)).

Thus the correlation results R_(k) may be used to determine a preferredhypothesis H_(#)regarding evolution of the phase {ϕ(t_(n))}_(#)duringthe time period of coherent integration. It may be possible, in thisway, to determine corresponding preferred sequences for one or more ofthe phase parameters that determine {X(t_(n))}_(#)and {ϕ(t_(n))}_(#)suchas receiver frequency error {f_(Rerr)}_(#), {v_(r)}_(#), {u}_(#),{v_(s)}_(#), {δr_(s)}_(#), {δr_(r)}_(#)etc.

The hypotheses {H_(k)} may, for example, be based on the differentevolutions (variations in time) of one or more phase parameters that aredependent upon a frequency deviation of the local oscillator of thereceiver {f_(Rerr)}; orientation of the receiver over the time period{h}; movement of the receiver over the time period {v_(r)}, {δr_(r)};movement of a source of the digital signals over the time period{v_(s)}, relative position of the receiver and source over the timeperiod {u}; the relative speed v_(u) of the receiver towards the signalsource.

The correlation results R_(k) may be used to determine a preferredhypothesis H_(#)regarding the evolution of the phase{ϕ(t_(n))}_(#)during the time period of coherent integration. Apreferred correlation result is selected determining a correspondingpreferred hypothesis regarding evolution of the phase during the timeperiod. In one example, one of the correlation results R_(k=#)isselected as one preferred correlation result and corresponding onepreferred hypothesis H_(#)regarding evolution of the phase during thetime period of coherent integration. This approach may, for example, beused when the phase sequences {ϕ(t_(n))}_(k) are based on estimatedtrajectories of the receiver as the hypotheses.

In another example, each hypothesis H_(k) speculates that the receiverhas moved a certain amount. This effectively hypothesises a sequence forv_(r)(t). Different hypotheses are generated for different amounts ofmovement and also for different signal sources. In this example, foreach movement hypothesis the corresponding correlation results R_(k) foreach of the multiple signal sources are combined to provide a jointscore for each hypothesis over all signal sources. The hypothesisresulting in the highest joint score across the signal sources in use isselected as a preferred hypothesis H_(#)regarding movement of thereceiver. Thus if calibrating a phase parameter (e.g. heading error) wehave the correct one when all visible signal sources have maximumcorrelation results on their expected lines of sight.

The selection of a preferred correlation result or preferred correlationresults may be based upon a comparison of the multiple respectivecorrelation results to select one or more.

The selection may, for example, optimize a phase-dependent ormotion-dependent parameter value.

Selection may for example optimize a maximum cumulative power for onesignal source, for all signal sources or for a selected sub-set ofsignal sources.

In some circumstances the highest power may result from a directlyreceived signal from the original signal source e.g. satellite. Forexample, it may be possible to consider only direct line of sightsignals by constraining u to a range of values likely to be aligned withr_(s)−r_(r), where r_(s) is a vector displacement of the original signalsource from an origin and r_(r) is a vector displacement of the receiverfrom the origin.

In other circumstances the highest power may result from an indirectlyreceived signal (a reflected signal). For example, it may be possible toconsider only reflected signals by constraining u to a range of valuesnot likely to be aligned with r_(s)−r_(r),

In other circumstances the highest power may result from a signal sentby an unauthorised source (a spoofed signal). For example, it may bepossible to recognise such a signal by constraining u to a range ofvalues not likely to be aligned with r_(s)−r_(r), or to filter out sucha signal by constraining u to a range of values likely to be alignedwith r_(s)−r_(r).

Overview

The phase (motion) compensated correlation may involve constructing verylarge phase (motion)-compensated code words and then testing smallvariations in their construction, based on a parametric model of phasevariation, in order to calibrate/update/monitor system parameters thatare varying slowly. This is particularly effective in the presence ofsevere multipath and in difficult attenuation conditions such asindoors.

Small variations are adjustments expected to be the smallest adjustmentsthat are large enough to elicit a change in result power that cannot beattributed to just measurement noise. By slightly adjusting the systemparameters it is possible to maximise the power and maintain goodcalibration of the system parameters.

Varying slowly means varying slower than the sampling rate of the datasignal. The variation may be modelled and predicted, for example, usinga model in which a parameter varies linearly with time on the timescaleof the coherent integration length T or using another model, forexample, one in which a parameter (for example receiver frequencyreference frequency error) varies as an n-order polynomial (where n is avalue greater than or equal to 2). For example, the local receiverfrequency reference might be exhibiting a gradual linear drift infrequency across the coherent integration time T or a polynomial driftin frequency across the coherent integration time T. For example thestep length estimate might be too great by a fixed value. The steplength may gradually shorten as the user gets tired, and this gradualshortening in step length will be over a timescale much greater than thecoherent integration time T.

The “parametric model” refers to a set of equations which governs howour parametric information (e.g. sensor measurements) are translatedinto the time-frequency space, ultimately providing a(measurement-based) prediction of the frequency and phase evolution ofthe signal as received at the receiver. The equations may containparameters—both time variant and invariant—the values of which areinitially unknown or uncertain, but which may bedetermined/calibrated/optimised as described.

For example, if the measurements are accelerations and rotation ratesfrom an inertial measurement unit attached to the receiver, the set ofequations governing how these are translated first to velocities, andultimately to Doppler frequency shifts, are the inertial navigationequations and various coordinate frame transformations. Parameterswithin the inertial navigation equations that may be optimised couldinclude accelerometer and gyro biases, scale-factors and alignments. Theoptimisation of such parameters can be achieved by the methodsdescribed. The underlying set of equations, the model, does not change,meaning that our optimal frequency and phase evolution is always fullyconsistent with the physical model.

The construction of the large motion (or phase) compensated code wordsare based on (consistent with) underlying parametric models. Theresultant frequency (and phase) evolution is entirely consistent withthe underlying model, and cannot simply follow any path within thetime-frequency space.

By performing the correlation in parallel for multiple differentparameter sequences {p(t_(n))} over the time period one is performingthe correlation using different hypotheses H_(k) regarding the evolutionof the phase through the time period. Each hypothesis H_(k) is definedby a different phase parameter sequence {p(t_(n))}_(k).

Single Parameters

If one assumes that all phase parameters p(t) are known or well definedover the period T except for one parameter p_(i)(t), then it may bepossible to find the parameter sequence {p_(i)(t_(n))} over the periodthat optimizes R. The optimal value may be determined by optimising ascore function based on the correlation results.

Further optimisation schemes may also be employed, including those thatalso weight the optimisation score using prior models and estimates ofthe errors associated with different measurements and parameters.

In one example, the optimal score may be found by determining where thecorrelation power is maximal. Depending on the scenario it may bedesirable to find a local maximum, or the global maximum constrained bythe parametric model. For example when using an attenuated LOS signal tocalibrate a system parameter the local maximum is used, as the globalmaximum across the entire search space might be associated with astronger reflected signal.

The hypothesis testing method involves correlation of a digital signal{S(t_(n))} received by a receiver during a first time period (e.g. t=0to t=T), via a communications channel, and the same correlation code CMcompensated using different multiple putative phasor sequences{X(t_(n))}_(k) to produce a correlation result R_(k) for each differentmultiple putative phasor sequence {X(t_(n))}_(k)

Each phasor sequence {X(t_(n))}_(k) comprises multiple phasors X(t_(n))each representing a phase ϕ(t_(n)) at a defined time t_(n) during thefirst time period (t=0 to t=T).

The multiple putative phasor sequences {X(t_(n))}_(k) are different(index k) in that each putative phasor sequence {X(t_(n))}_(k) is basedon a different hypothesis H_(k) regarding the evolution of the phasesequence {ϕ(t_(n))}_(k) through the defined times t_(n) during the firsttime period.

The method uses the correlation results R_(k) to determine a preferredhypothesis H_(#)regarding evolution of the phase sequence{ϕ(t_(n))}_(#)during the first time period.

Each phase sequence {ϕ(t_(n))}_(k) comprises multiple phase valuesϕ(t_(n)) for different times t_(n) within a single correlation code orconcatenated correlation code. It represents an end-to-end multi-steppath through a phase-time space. The hypothesis H_(k) (defined byparameter sequence {p(t_(n))}_(k)) represents a model of a possibleend-to-end multi-step path through a phase-time space which is assessedover its whole length simultaneously. An assumed or measured model(multi-step path) of phase sequence {ϕ(t_(n))}_(k) over time is usedrather than a brute force exhaustive search. The model defines theevolution of the phase value ϕ(t_(n)) during the time period ofcorrelation (coherent integration) such that optimisation of thecorrelation result is at all times constrained by and consistent withthe underlying model.

Multiple Signals

In some instances the optimum phase parameter sequence{p_(i)(t_(n))}_(#)may be determined using a single signal source wherethe signal received is strong enough. The single signal source used maybe a selected one of the signal sources available or the only signalsource available.

The optimum phase parameter sequence {p_(i)(t_(n))}_(#)may be determinedusing multiple signal sources. The multiple signal sources used may beall of the signal sources available or a selected sub-set of theavailable signal sources.

For example, a sub-set of the available signal sources may be selectedby selecting those signal sources that have a maximum correlation resultfor the same k (i.e. for the same hypothesis H_(k) as applieddifferently to each received signal).

Multiple signal sources may be used to determine the optimum phaseparameter sequence {p_(i)(t_(n))}_(#)by considering the correlationresults R_(k) for each signal source.

For example, optimum phase parameter sequence {p_(i)(t_(n))}_(#)may bedetermined by identifying that multiple signal sources have a maximumcorrelation result max R_(k) for the same k (i.e. for the samehypothesis H_(k) as applied differently to each received signal whichprovides the optimum k=#defining {p_(i)(t_(n))}_(#)).

In one example, {p_(i)(t_(n))} may be found separately for each signalsource by determining the value of H_(k) where the power is maximal foreach signal. For example one can use a numerical optimisation method tomaximise the coherent correlation value for a set of possible phaseparameter sequences, i.e. {p_(i)(t_(n))}_(#)=argmax_({p) _(i) _((t) _(n)_()}k)|R_(k) ^((l))| were | is the signal source under consideration,and where argmax in this instance is a function which returns theparameter sequence {p_(i)(t_(n))}_(#)resulting in the maximumcorrelation value.

In some examples, {p_(i)(t_(n))} may be found collectively for multiplesignals by determining the value of H_(k) where the combined power ofthe signals is maximal, i.e. {p_(i)(t_(n))}_(#)=argmax_({p) _(i) _((t)_(n) _()}k) Σ_(t) |R_(k) ^((l))|². Here the objective function is thetotal signal power, using the non-coherent correlation of the individualsignals. It will be appreciated that other object functions, for exampleusing the coherent total correlation of the signals, could be used.

Multiple Parameters

The optimisation described above considers optimisation of a singlephase parameter. It is also possible to perform such optimisationsimultaneously over two or more parameters.

If one assumes that all phase parameters p(t) are known or well definedover the period T except for a plurality of parameters p_(i)(t), then itmay be possible to find the phase parameter sequences {p_(i)(t)} overthe time period that optimizes R.

For simplicity of explanation the plurality of parameters p_(i)(t), willbe referred to as parameters p₁(t) and p₂(t). However, it should berecognised that in some but not necessarily all examples, the pluralityof parameters p(t) may be more numerous than two.

By performing the correlation in parallel for multiple differentparameter sequences {p₁(t_(n))}_(j), {p₂(t_(n))}_(k) over the timeperiod, one is performing the correlation using different hypothesisH_(j,k) regarding the evolution of the phase through the time period.Each hypothesis H_(j,k) is defined by a different combination{p₁(t_(n))}_(j){p₂(t_(n))}_(k) of sequence {p₁(t_(n))}; andsimultaneously {p₂(t_(n))}_(k)

In one example it is possible to find the optimum combination ofparameter sequences ({p₁(t_(n))}_(#){p₂(t_(n))}_(#)) that produces theoptimum phase sequence {ϕ(t_(n))}_(#)by maximising the totalnon-coherent sum of the correlation power over all signal sources({p₁(t_(n))}_(#), {p₂(t_(n))}_(#))=argmax_({p) ₁ _((t) _(n) _()}) _(j)_(,{p) ₂ _((t) _(n) _()}) _(k) Σ_(l) |R_(j,k) ^((l))|²

while the signal sources and receiver are in relative motion. This maybe detected or assumed, for example, because the signal sources are inconstant motion (e.g. GNSS satellites).

Approach

The hypothesis testing method involves correlating a sequence {S(t_(n))}of a digital signal received by a receiver during a first time period(e.g. t=0 to t=T), via a communications channel, and the samecorrelation code C(t) compensated using different multiple j,k putativephasor sequences {X(t_(n))}_(j,k) to produce a correlation resultR_(j,k) for each different multiple putative phasor sequence{X(t_(n))}_(j,k)

Each phasor sequence {X(t_(n))}_(j,k) comprises multiple phasorsX(t_(n)) each representing a phase X(t_(n)) at a defined time t_(n)during the first time (t=0 to t=T).

The multiple j,k putative phasor sequences {X(t_(n))}_(j,k) aredifferent (indices j,k) in that each putative phasor sequence{X(t_(n))}_(j,k) is based on a different hypothesis H_(j,k) regardingthe evolution of the phase {ϕ(t_(n))}_(j,k) through the defined timest_(n) during the time period.

The method uses the correlation results R_(j,k) to determine a preferredhypothesis H_(#)regarding the evolution of the phase{ϕ(t_(n))}_(#)during the time period of coherent integration(correlation) T.

Each phase sequence {ϕ(t_(n))}_(j,k) comprises multiple phase valuesϕ(t_(n)) for different times t_(n) within a single correlation code orconcatenated correlation code. It represents an end-to-end multi-steppath through a phase-time space. The hypothesis H_(j,k) (defined by theparameter sequence combination {p₁(t_(n))}_(j), {p₂(t_(n))}_(k))represents a model of a possible end-to-end multi-step path through aphase-time space which is assessed over its whole length simultaneously.An assumed or measured model (multi-step path) of phase value ϕ(t_(n))over time is used rather than a brute force exhaustive search. The modeldefines the evolution of the phase value ϕ(t_(n)) during the time periodof correlation (coherent integration) such that optimisation of thecorrelation result is at all times constrained by and consistent withthe underlying model.

Applications

Phase-compensated correlation can provide high confidence about certainphase parameter values p(t) such as heading and local oscillator offsetwith much less data than competing techniques, because the data providedby phase-compensated correlation has a much higher signal strength andis much cleaner (multipath mitigated). Phase-compensated correlation canmake use of very weak signals in difficult environments where standardmethods cannot work as such methods are unable to extract any signalwhatsoever. Phase-compensated correlation also works in completelybenign signal environments with unobstructed line of sight to signalsources.

An optimum phase parameter sequence {p_(i)(t_(n))}_(#)can be calculatedusing different objective functions and optimisation criterion fordifferent applications.

The optimum phase parameter sequence {p_(i)(t_(n))}_(#)may for examplebe a kinematic parameter sequence, for example a receiver kinematicparameter sequence or a relative displacement kinematic parametersequence.

The optimum phase parameter sequence {p_(i)(t_(n))}_(#)may be used fordetermining a trajectory of the receiver for example {v_(r)(t_(n))} whenp_(i)(t)=v_(r)(t). The sequence {v_(r)(t_(n))} may also be determined bydifferentiating {v_(r)(t)}.

The optimum phase parameter sequence {p_(i)(t_(n))}_(#)may be used fordetermining a position of the receiver {r_(r)(t_(n))} whenp_(i)(t)=r_(r)(t) The sequence {r_(r)(t_(n))} may also be determined byintegrating {v_(r)(t_(n))}.

The optimum phase parameter sequence {p_(i)(t_(n))}_(#)may be used fordetermining the length of a step taken by a user carrying the receiver{δr_(step)(t)} when p(t)=δr_(step)(t). User step length δr_(step) isfundamental to the good operation of personal dead-reckoning navigation.δr_(step) is the distance travelled over the ground between step events(where step events may be detected, for example, from accelerometertraces).

The optimum phase parameter sequence {p_(i)(t_(n))}_(#)may be used fordetermining a heading of the receiver {h(t_(n))} when p_(i)(t)=h(t). Forexample, considering a GNSS (such as GPS) a heading error between theframe of reference of inertial sensors in the receiver, and the frame ofreference defined by the GNSS satellites, can be resolved with 1 secondof data and as little as a few tens of centimetres of motion.

The optimum phase parameter sequence {p_(i)(t_(n))}_(#)may be used fordetermining line of sight u_(LOS) when p_(i)(t)=u. If the phasorsequence, associated with a trial direction of signal arrival u, resultsin signal detection, then a signal is arriving from that direction. Ifthis direction corresponds to the expected light of sight directionu_(LOS) then we can treat this signal as the direct path from the signalsource. If test u vectors in other directions result in signaldetection, this may indicate that the received signal is a reflectedsignal or a spoofed signal. The identification of a signal as areflected signal or spoofed signal may enable it to be excluded from use(rejected).

The optimum phase parameter sequence {p_(i)(t_(n))}_(#)may be used tocalibrate initial conditions, biases and offsets for differentsystems/system components (e.g. inertial sensors, frequency references,Attitude and Heading Reference System (AHRS), compasses, other RF-basednavigation aids). There is no need for the receiver to be static duringthe process and there is no need for the user to follow a definedprocedure. The process may be transparent to a user of the receiver (notinvolve the user).

Examples of components that can be calibrated include one or more of:frequency oscillators which may enable the use of low-cost frequencyoscillators, human step measuring sensor, inertial sensors,magnetometers, gyroscopes and accelerometers.

The optimum {p_(i)(t_(n))}_(#)may be used for determining anoscillator/frequency reference frequency error of the receiver whenp_(i)(t)=f_(Rerr)(t).

Use Cases

Motion-compensated correlation (see Equation 6) couples to energy from acertain direction and washes out the energy in other directions (whenthe receiver is moving).

A smartphone may be placed at an arbitrary orientation relative to theactual direction of motion, for example when in a pocket or bag. Theoffset between the smartphone compass heading and the actual user motionheading needs to be determined to allow human motion modelling to assisttrajectory reconstruction. We note this heading error term h

While the user is moving outside and GNSS signals are readily availableat standard signal level, a range of trial trajectories similar to theinitial heading estimate and representing a range of heading estimatescan be tested using supercorrelation, with the joint gain of thereceiver GPS signal correlation peaks over all incoming signals givingthe metric for optimisation.

Supercorrelation refers to using a phasor sequence {X(t_(n))} comprisingmultiple phasors X(t_(n)) each representing a phase ϕ(t_(n)) that has alength longer that the correlation code word length. For example, if onewere doing a 1 second supercorrelation then one might use an inertialmeasurement unit running at 100 Hz to create a vector of 100 velocityvalues across the desired 1 second of time. One then interpolates thatto give us as many velocity values as there are radio samples in that 1second. Now in this “trial trajectories” aspect we choose togeometrically rotate the velocity sequence about a fixed point in orderto test a bunch of heading corrections (a bunch of slight variations tothe inertial measurement unit heading estimating).

By using all signals jointly the method is robust to multipathinterference and reflected signals because only the true headingestimate will result in a simultaneous summing of the energy from allsignal sources in a single score value for that orientation.

Alternatively a simple linear compression or dilation of the trajectoryin the direction of each signal source can be tested by adjusting afixed frequency offset added to the base frequency used to generate theSupercorrelation phasor sequence. By optimising for each signal sourceb=1, 2 . . . B in this manner, a set of B simultaneous equations can beconstructed where the free parameter h is the heading error to becalibrated, and the input measurements to the equation set are thefrequency shifts determined by performing this process for eachtransmitter. These are just two examples of the optimisation methodsthat might be employed but are not expected to be an exhaustive list.

The benefit of this approach over existing methods is the multipathmitigation and signal boosting. Both mean we can calibrate moreconfidently and with less data when in difficult signal environments(LOS plus reflections, some signals not LOS, etc).

Plotting the supercorrelation gains of the correlator at a given momentfor some long phase compensation sequence (e.g. 1 second) and testing arange of some parameter of interest; in this example, varying a smallconstant term f_(test) being added to the frequency sequence F(t)predicted for the incoming signal. The power of the correlation resultwill be maximum at the correct F(t)+f_(test) estimate. If the system iswell calibrated then f_(test) will be zero, or very close to zero withinmeasurement noise, for each incoming signal. If there is a commonf_(test) for each signal then there is a common frequency error (e.g. alocal frequency reference frequency offset). This common frequency errorcan be estimated by taking the mean of the f_(test) values produced byeach signal. If the f_(test) values are distinctly different for eachsignal, then there is at least one parameter needing calibration that isnot a common error. In some cases the distribution of the f_(test)values from each incoming signal can be mapped directly back to theparameter of interest. A heading error is an example of such a term,since there is a direct mapping between a receiver heading error and atrigonometric correction in all line-of-sight vectors between thereceiver and all sources. Note that estimating the heading error in thisway may still leave a residual, common non-zero value of f_(test). Inthis case it is likely that the remaining value of f_(test) represents areceiver frequency error f_(Rerr).

In this way multiple parameters can be calibrated at the same step byexploiting the signal geometry and knowing that some parameters willcause common errors to all signal source channels (such as the receiverfrequency error f) and others will cause a particular non-common-to-allpattern of errors that allow the parameter error in question to beobserved and tuned.

In a system that is not well calibrated there are errors in thepredicted phases used for correlation. Since these values are predictedusing a range of other parameters (receiver location, receiver time,satellite orbit data, receiver frequency reference error estimate,receiver-motion estimate) we can use this distribution of errors acrossthe satellite measurements to optimise out an error in a parameter knownto be the likely source of error.

We can additionally or alternatively perform hypothesis testing for theparameters of interest. For example, instead of shifting thephase-compensated phasor sequences to then infer corrections to theunderlying system parameters, we can instead change the underlyingsystem parameters to directly calculate bespoke phase-compensated phasorsequences for each hypothesis (e.g. heading offset estimate) anddetermine the best hypothesis as described above.

In the scenarios where the effects of all frequency reference-relatedfrequency errors are absent or have been compensated, the sequence ofphases {ϕ(t_(n))} used in the calculation of the phase-compensatedphasor sequence {X(t_(n))} are determined by a sequence of velocities{v_(u)(t_(n))} that represent an hypothesis regarding evolution of theDoppler frequency shift during a first time period t=0 to t=T. Selectionof the correlation result with the highest cumulative power, selects thecorresponding hypothesis regarding evolution of the Doppler frequencyshift during the first time period as the best hypothesis. Thecorresponding sequence of velocities {v_(u)(t_(n))} that represents thebest hypothesis is also identified and may be used to calculate achanging position of the receiver.

Multipath Interference and Signal Selection

The preceding paragraphs have described phase-compensated correlation ofone or more signals from one or more sources. The selection of whichsignal or signals to use may be based on one or more criteria.

It may, for example, be desirable to discriminate between line of sightsignals and reflected signals from the same signal source. Reflectedsignals suffer from a delay. This delay may be modelled as an unknownoffset in phase.

It may be possible to disambiguate between a line of sight signal and areflected signal because the line of sight signal has least delay andthe different paths have different delay. This disambiguation ispossible using traditional correlation methods when the delay is greaterthan the coherence length of the signal. The coherence length is relatedto the bandwidth of the signal, and for GPS L1 signals is approximately300 metres. Phase-compensated correlation codes (Supercorrelators) thatcouple strongly to the line of sight signals can be used to attenuatereflected signals thereby removing multipath interference, even fromreflected signals with much shorter delays than the coherence length ofthe signal.

It may also be possible to disambiguate between line of sight signalsand first reflected signals that have arrived by a similar but not thesame first path and second reflected signals that have arrived by asimilar but not the same second path because the line of sight signalshave least delay and the first reflected signals as a group have a delaythat is different from the second reflected signals as a group. Byidentifying such groupings it is possible to select or exclude fromselection signals that have arrived within certain delays.

It is possible to compensate for a group delay by applying a commonphase offset before or after motion-compensated correlation. The use ofmotion-compensated correlation applied to a sub-set of the receivedsignals that have a similar group delay may increase signal to noiseratio and enable determination of one or more phase parameters which maythen be used to further improve signal to noise.

In some circumstances, instead of compensating for a group delay, thesource signals of different groups may be treated as signals fromdifferent sources.

It may, additionally or alternatively, be desirable to discriminatebetween signals from the same signal source received from differentdirections. The use of phase-compensated correlation using different umay be used for this purpose. It may be desirable for the receiver to bemoving so that there are significant phase changes for relatively smallchanges in the orientation of u.

This may be used to discriminate between a line of sight signal and areflected signal.

This may also be used to discriminate between a signal received from anexpected direction and a signal received from an unexpected direction.This may enable the signal from the unexpected direction to be rejectedas a spoofed signal.

It may for example be desirable to select a particular source of signalsbecause its line of sight vector u_(LOS) has a certain orientationrelative to the receiver or its position and/or movement has some otherrelationship to position and/or movement of the receiver.

Multipath

It may, in some circumstances be desirable to use (select) the strongestsignal whether or not it is a reflected signal. A reflected signal hasan unknown delay but may be used (selected) for phase-compensatedcorrelation (and determination of the delay using correlation). Forexample, a reflected signal can still be useful in determining the localfrequency reference error.

It may, in some circumstances be possible to use (select) multiplereflected signals even with extreme delays (such as a delay longer intime than the inverse of the signal bandwidth) when the selectedmultiple reflected signals received have equivalent delays. In such acircumstance the delayed signal can still be useful in determining thelocal frequency reference error. Examples have been given above on howto determine such an offset error.

The selection of a reflected signal for use may occur beforephase-compensated correlation (if there is sufficient information todiscriminate the signal) or after phase-compensated correlation.

It may, in some circumstances be desirable to use (select) the strongestsignal line of sight signal(s).

Sample Selection

In some circumstances it may not be desirable to perform a correlation,for example a phase-compensated correlation, for every sample of thereceived signal. A selection process may occur to determine whichsub-set of the samples of the received signal are to be used or notused, or to determine periods of time during which it is decided thatcorrelation is carried out or not carried out.

In one example, the selection may be that intermittent samples arecorrelated. This may be used to reduce processing power. When applied tophase-compensated correlation it may be used to obtain some of thebenefits of long term coherent integration but at a coarser scale thanat each sample.

In one example, the selection may be that one or more samples are notused for phase-compensated correlation or that the result ofphase-compensated correlation is not used for those one or more samples.For example, if there is detection of an anomaly (an event thatinterferes with phase-compensated correlation) for a certain time period(unused time period) then the samples coinciding with that anomaly(coincident samples) may not be used (not used for phase-compensatedcorrelation or the result of phase-compensated correlation is not usedfor those one or more samples). In one example, an accelerometer profilemay be used to identify a period of time when there is rapidacceleration or deceleration which may impact operation of a crystaloscillator and then not use the coincident samples for that period oftime. In another example, periods when a heel strike occurs while aperson carrying the receiver is walking may be used to determine timeperiods for which coincident samples are not used. In another example,very rapid turns, may result in inaccurate readings from a gyroscope.

An anomaly may be used to calibrate a parameter value of the parametricmodel. For example shocks can introduce a phase change in the receiverfrequency reference (local oscillator). The magnitude of the strikemeasured by an accelerometer could be used to correct the frequency ofthe receiver frequency reference (local oscillator). The accelerometermay be used to infer the shock-dependent variations in the receiverfrequency reference output.

Parameter Calibration by Signal Selection

The phase depends on v_(u)=(v_(s)−v_(r))·u.

Assuming f_(Serr) and f_(Rerr) are zero or compensated for, if thesignal is selected and motion of the receiver controlled or directedsuch that v_(s) (the signal source velocity) and v_(r) (the receivervelocity) are orthogonal and v_(r) is along u_(LOS) then the phase islinear in v_(r). Therefore correlation of a signal from the source mayprovide v_(r) if the receiver moves relative to the source.

Alternatively a source may be selected whose motion v_(s) is orthogonalto u e.g. an overhead GNSS satellite.

Alternatively a motion of the receiver may be controlled or directedsuch that it has motion v_(r) orthogonal to u or such that v_(s)−v_(r)is orthogonal to u.

Parameter Variation Modeling

It may be desirable to model the time evolution of a phase parameter, sothat the model can be used to provide phase parameter values for eachdata sample,

For example, measurements may be made of the phase parameter value lessoften than each data sample and those measurements may be used tocalibrate a model of time evolution of the phase parameter.

The measurements and calibration may, for example, be madeintermittently according to a schedule, for example periodically oraccording to some other criteria, for example, based on a stability of aphase parameter measurement system.

In one example, the receiver frequency reference frequency error (andconsequently the phase variation arising from it) may be modelled as alinear equation in time t or a polynomial equation of order n in time t,where n is equal to or greater than 2.

By performing multiple distinct measurements of the receiver frequencyreference frequency error, it is possible to define the polynomialequation.

The receiver frequency reference frequency error may, for example, bemeasured using hypothesis testing, motion-compensated correlation of agood signal or correlation of a signal from an unobstructed satellite,for example an overhead satellite.

The measurements and calibration of the polynomial for the receiverfrequency reference frequency error may, for example, be madeintermittently according to a schedule, for example periodically oraccording to some other criteria, for example, based on stability of thereceiver frequency reference. For example, a significant change inambient temperature may trigger a definition or redefinition of thepolynomial defining the receiver frequency reference frequency error.

In some examples, the order n may be fixed. In other examples, the ordern may be variable.

Long Codes

FIG. 5 illustrates an example of a correlation code generator 340 thatprovides a correlation code 341 that may be used for correlation asdescribed above. The correlation code 341 is a long correlation code asdescribed below. A short code generator 470 produces a correlation code341′. A long code generator 472 concatenates the correlation code 341′multiple times to produce the long correlation code 341. The longcorrelation code may be stored in a buffer memory 474 that is ofsufficient size to temporarily store a concatenation of multiplecorrelation codes 341′. FIG. 6 illustrates an example of a long digitalsignal buffer 480 that temporarily stores a received digital signal 222that may be used for motion-compensated correlation as described above.This is a buffer memory 474 that is of sufficient size to temporarilystore received digital signal 222 that has a duration as long as thelong correlation code 341.

The digital signal 222 is a long digital signal, the correlation code341 is a long correlation code, the phase-compensated correlation code322 is a long phase-compensated correlation code.

The long digital signal 222, the long correlation code 341 and the longphase-compensated correlation code 322 have the same length. Each havinga duration greater than a length of the correlation code word e.g.greater than 1 ms for GPS or greater than 4 ms for GALILEO. For example,the duration may be N*1 ms or M*4 ms where N, M are natural numbersgreater than 1. It may in some examples be possible to change theduration, for example, in dependence upon confidence of receiver-motionmeasurement when performing motion-compensated correlation. It may insome examples be possible to increase and/or decrease N or M. It may insome examples be possible to select between having a duration N*1 ms orM*4 ms. A longer duration increases correlation time providing bettergain.

The long correlation code 341 is a concatenation of multiple ones of asame first correlation code 341′.

The first correlation code 341′ may be a standard or reference code e.g.a Gold code, Barker code or a similar that has a fixed period T andpredetermined cross-correlation properties.

A long phase-compensated correlation sequence 422 may be referred to asa supercorrelation sequence. A supercorrelation sequence may be a longphase-compensated phasor sequence or a long phase-compensatedcorrelation code (phasor adjusted).

FIG. 7 illustrates an example of a phase-compensated correlator 300comprising multiple phase-compensated correlation sequence (PCCS)generators 320.

The phase-compensated correlator 300 may also optionally comprise aphase-compensated correlation sequence system 500 comprising aphase-compensated correlation sequence (PCSS) storage system 420, aphase-compensated correlation sequence (PCCS) re-use system 450 andmultiple phase-compensated correlation sequence (MCCS) generator 320.

The FOGS re-use system 450 determines if and what phase-correlationshould be performed on a received digital signal 222, The PCCS re-usesystem 450 receives as an input the parameter information 361 which maybe used to determine whether a current in use phase-compensatedcorrelation sequence 422 should be re-used for phase-compensatedcorrelation of a received digital signal 222 (re-use current), and/orwhether a previously used/stored phase-compensated correlation sequence422 should be re-used/used for phase-compensated correlation of areceived digital signal 222 (PCCS access) and/or whether a newphase-compensated correlation sequence 422 should be generated forphase-compensated correlation of a received digital signal 222 (PCCSgeneration) and/or whether phase-compensated correlation of a receiveddigital signal 222 should be suspended (suspend).

In some but not necessarily all examples, if the parameter information361 is determined to represent a state (e.g. an assumed or measuredmovement of the receiver 200) that is the same as or corresponds to theimmediately preceding state (e.g. an assumed or measured movement of thereceiver 200) then it may be determined that the phase-compensation forthe receiver 200 is invariant (repeated) and the currently usedphase-compensated correlation sequence 422 may be re-used via there-used.

In some but not necessarily all examples, if the parameter information361 is determined to represent a state (e.g. an assumed or measuredmovement of the receiver 200) that is the same as or corresponds to astate (e.g. an assumed or measured movement of the receiver 200) forwhich there exists a stored phase-compensated correlation sequence 422associated with that state then that stored phase-compensatedcorrelation sequence 422 is accessed in the addressable memory and usedvia the PCCS storage system 420. The accessed stored phase-compensatedcorrelation sequence 422 may be a previously used and/or previouslygenerated phase-compensated correlation sequence 422. It may have beenstored by the PCSS storage system 420 in an addressable memory forre-use.

Each of the multiple phase-compensated correlation code generators 320generates a long phase-compensated correlation code 322 which is a longcorrelation code 341 that has been compensated, before correlation,using the same long phase-compensated phasor sequence 332.

A first one of the multiple phase-compensated correlation codegenerators 320 produces an early long phase-compensated correlation code322 which is a long correlation code 341 that has been compensated,before correlation, using the same long phase-compensated phasorsequence 332 and time shifted to be early.

A second one of the multiple phase-compensated correlation codegenerators 320 produces a present (prompt) long phase-compensatedcorrelation code 322 which is a long correlation code 341 that has beencompensated, before correlation, using the same long phase-compensatedphasor sequence 332.

A third one of the multiple phase-compensated correlation codegenerators 320 produces a late long phase-compensated correlation code322 which is a long correlation code 341 that has been compensated,before correlation, using the same long phase-compensated phasorsequence 332 and time shifted late.

Each of the early long phase-compensated correlation code, present(prompt) long phase-compensated correlation code and late longphase-compensated correlation code are separately correlated with thesame long digital signal 222.

The phase-compensated correlator 300 is suitable for use in a globalnavigation satellite system (GNSS) where the received digital signal 222is transmitted by a GNSS satellite. The phase-compensated correlator 300may be part of a GNSS receiver 200.

In some but not necessarily all examples, down-conversion of a receivedsignal before analogue to digital conversion to create the digitalsignal 222 occurs, in other examples it does not. Where down-conversionof a received signal before analogue to digital conversion to create thedigital signal 222 occurs, in some but not necessarily all examples, thedown-conversion is independent of a measured movement of the receiver200 and is not controlled in dependence upon the measured movement of areceiver 200 of the received signal.

In some but not necessarily all examples a modulation removal block 510may remove any data that has been modulated onto the signals beingcoherently integrated using the phase-compensated correlator. An exampleof this is the removal of the navigation bits from a received GNSSdigital signal 222′ to produce the digital signal 222 processed by thephase-compensated correlator 300.

In this example, the correlation code concatenated to produce the longcorrelation code 341 is a chipping code or a pseudorandom noise code. Itmay for example be a Gold code.

Each GNSS satellite may use a different long correlation code 341 insome examples. Multiple phase-compensated correlators 300 may beprovided and may be assigned to different satellites. Aphase-compensated correlator 300 then performs phase-compensatedcorrelation for the assigned GNSS satellite.

In some examples, movement of the assigned satellite may be compensatedby using the line of sight relative velocity v_(u) between the receiver200 and the assigned satellite. In other examples, movement of theassigned satellite may be compensated by using closed control loop asillustrated in FIG. 8 . Correlating the digital signal 222 provided bythe receiver 200 with the long phase compensated correlation code 322additionally uses one or more closed control loops 610, 620 formaintenance of code-phase alignment and/or carrier-phase alignment 620.

A control system 254 uses the results 312 of phase-correlatedcorrelation to provide a closed-loop control signal 610 and/or a closedloop control signal 620.

A closed-loop control signal 610 controls a phase adjust module 600 toadjust the phase of the phase-compensated correlation codes 322 tomaintain carrier phase alignment.

A closed-loop control signal 620 controls each of the multiplephase-compensated correlation code generators 320 for the satellite tomaintain code phase alignment.

FIG. 9 illustrates an example of how phase-compensated correlation codegenerators 320 may maintain code-phase alignment via a closed loopcontrol signal 620. A numerical controlled oscillator 632 receives thecontrol signal 620 and controls the long correlation code generator 340using the short code generator 470 and a shift register 634 that buffersthe long correlation code 341 and simultaneously operates as long codegenerator 472 and long code buffer 474 for the multiplephase-compensated correlation code generators 320 used for a particularsignal source e.g. satellite.

FIGS. 10A and 10B illustrate different examples of a phase parametermodule 360 for producing phase parameter information 361, for example,indicative of one or more time-varying parameters {p_(i)(t_(n))}.

For example in some but not necessarily all examples, FIGS. 10A and 10Billustrate different examples of a receiver-motion module 360 forproducing a movement signal 361 indicative of a movement of the receiver200 during a particular time duration. The receiver-motion module 360illustrated in FIG. 10A produces a movement signal 361 indicative of ameasured movement of the receiver 200. The receiver-motion module 360illustrated in FIG. 10B produces a movement signal 361 indicative of anassumed movement of the receiver 200.

The movement signal 361 may be a parameterized signal defined by a setof one or more parameters.

The receiver-motion module 360 may, for example, be used to determine avelocity of a pedestrian or a vehicle

The receiver-motion module 360 that measures the receiver movement asillustrated in FIG. 10A may have a local navigation or positioningsystem that tracks motion of the receiver 200, such as a pedestrian deadreckoning system, an inertial navigation system, a visual trackingsystem, or a radio positioning system

An inertial navigation system typically calculates velocity byintegrating acceleration measurements from inertial sensors such asmulti-axis accelerometers and gyroscopes.

A pedestrian dead reckoning system may detect a step from for example aheel strike, estimate step/stride length, estimate a heading, anddetermine a 2D position.

A radio positioning system may, for example, use WI-Fi positioningand/or Bluetooth positioning.

The receiver-motion module 360 that assumes the receiver movement,illustrated in FIG. 10B, may have a context detection system thatdetects a context of the receiver 200 such as a specific location at aspecific time and determines a receiver velocity on a past history ofthe receiver velocity for the same context. A learning algorithm may beused to identify re-occurring contexts when the receiver velocity ispredictable and to then detect that context to estimate the receivervelocity.

In other examples, FIGS. 10A and 10B may illustrate different examplesof a phase parameter module 360 for producing a phase parameter signal361 indicative of a time-varying parameter {p_(i)(t_(n))}. For example,the phase variation due to receiver frequency reference frequency error{ϕ_(f_Rerr)(t_(n))}.

As previously described, it may be desirable to model the time evolutionof a phase parameter, so that the model can be used to provide phaseparameter values for each data sample.

FIG. 11 illustrates an example of a record medium 700 such as a portablememory device storing a data structure 432. The data structure 432comprises: a phase-compensated correlation sequence 422 that is acombination of a (long) correlation code 341 and a (long)phase-compensated phasor sequence 332 or is a (long) phase-compensatedphasor sequence 332. The record medium 700 and the data structure 432enables transport of the phase-compensated correlation sequence 422. Thedata structure 432 may be configured as a data structure addressable forread access using a motion-dependent index.

In some but not necessarily all examples, the long phase-compensatedcorrelation sequence 422 is a combination of a long correlation code 341and a long phase-compensated phasor sequence 332 and the longcorrelation code 341 is a concatenation of multiple ones of the samestandard correlation code.

A controller 800 may be used to perform one or more of the beforedescribed methods, the before described blocks and or all or part of aphase-compensated correlator 300.

Implementation of a controller 800 may be as controller circuitry. Thecontroller 800 may be implemented in hardware alone, have certainaspects in software including firmware alone or can be a combination ofhardware and software (including firmware).

As illustrated in FIG. 12A the controller 800 may be implemented usinginstructions that enable hardware functionality, for example, by usingexecutable computer program instructions 710 in a general-purpose orspecial-purpose processor 810 that may be stored on a computer readablestorage medium (disk, memory etc) to be executed by such a processor810.

The processor 810 is configured to read from and write to the memory820. The processor 810 may also comprise an output interface via whichdata and/or commands are output by the processor 810 and an inputinterface via which data and/or commands are input to the processor 810.

The memory 820 stores a computer program 710 comprising computer programinstructions (computer program code) that controls the operation of allor part of a phase-compensated correlator 300 when loaded into theprocessor 810. The computer program instructions, of the computerprogram 710, provide the logic and routines that enables the apparatusto perform the methods illustrated in FIGS. 3 to 19 The processor 810 byreading the memory 820 is able to load and execute the computer program710.

An apparatus comprising the controller may therefore comprise:

at least one processor 810; and at least one memory 820 includingcomputer program code 710 the at least one memory 820 and the computerprogram code 710 configured to, with the at least one processor 810,cause the apparatus at least to perform causation of one, some or allthe methods described above or performance of one, some or all of themethods described above.

As illustrated in FIG. 12B, the computer program 710 may arrive at theapparatus 800 via any suitable delivery mechanism 700. The deliverymechanism 700 may be, for example, a non-transitory computer-readablestorage medium, a computer program product, a memory device, a recordmedium such as a compact disc read-only memory (CD-ROM) or digitalversatile disc (DVD) or solid state memory, an article of manufacturethat tangibly embodies the computer program 710. The delivery mechanismmay be a signal configured to reliably transfer the computer program710. The apparatus 800 may propagate or transmit the computer program710 as a computer data signal.

Although the memory 820 is illustrated as a single component/circuitryit may be implemented as one or more separate components/circuitry someor all of which may be integrated/removable and/or may providepermanent/semi-permanent/dynamic/cached storage.

Although the processor 810 is illustrated as a singlecomponent/circuitry it may be implemented as one or more separatecomponents/circuitry some or all of which may be integrated/removable.The processor 810 may be a single core or multi-core processor.

References to ‘computer-readable storage medium’, ‘computer programproduct’, ‘tangibly embodied computer program’ etc. or a ‘controller’,‘computer’, ‘processor’ etc. should be understood to encompass not onlycomputers having different architectures such as single/multi-processorarchitectures and sequential (Von Neumann)/parallel architectures butalso specialized circuits such as field-programmable gate arrays (FPGA),application specific circuits (ASIC), signal processing devices andother processing circuitry. References to computer program,instructions, code etc. should be understood to encompass software for aprogrammable processor or firmware such as, for example, theprogrammable content of a hardware device whether instructions for aprocessor, or configuration settings for a fixed-function device, gatearray or programmable logic device etc.

As illustrated in FIG. 13 , a chip set 840 may be configured to providefunctionality of the controller 800, for example, it may provide all orpart of a phase-compensated correlator 300.

The blocks illustrated in the FIGS. 3 to 19 may represent steps in amethod and/or sections of code in the computer program 710. Theillustration of a particular order to the blocks does not necessarilyimply that there is a required or preferred order for the blocks and theorder and arrangement of the block may be varied. Furthermore, it may bepossible for some blocks to be omitted.

The components of an apparatus or system required to perform one or moreof the before described methods, the before described blocks and or allor part of a phase-compensated correlator 300, need not be collocated,and data may be shared between components via one or more communicationlinks.

FIG. 14A illustrates one example of a system comprising a remote device1000 and a remote processing system 2000. The remote device 1000comprises the receiver 200 and the phase parameter module 360. The phaseparameter module 360 provides the parameter information 361 to theremote processing system 2000. In this example, the phase parametermodule 360 is a receiver-motion module 360 comprising receiver-motionsensors that provide receiver-motion sensor data (movement signal) asthe parameter information 361. The remote device 1000 is physicallydistant from the remote processing system 2000 comprising the controller800. The remote device 1000 and the remote processing system 2000communicate via communications link(s) 1500. The communications link(s)1500 may comprise of, for example, wireless communications (e.g. WiFi,BLE, Cellular Telephony, Satellite comms), cabled communications (e.g.Ethernet, landline telephone, fibre optic cable), physical storage mediathat may be transported between components (e.g. solid state memory,CD-ROM) or any combination thereof.

The digital signal 222 is provided by the remote device 1000 to theremote processing system 2000 via the communications link(s) 1500. Thereceiver-motion sensor data is provided as parameter information 361 bythe remote device 1000 to the remote processing system 2000 via thecommunications link(s) 1500.

The controller 800 of the remote processing system 2000 comprises thephase-compensated correlator 300 comprising the correlator 310 and thephase-compensated correlation sequence generator 320.

The phase-compensated correlation sequence generator 320 generates thephase-compensated correlation sequence 322 from processing of theparameter information 361, and the correlator 310 performsphase-compensated correlation of the digital signal 222 using thephase-compensated correlation sequence 322 to produce correlation result312.

The phase-compensated correlation sequence 322 may optionally be storedby a phase-compensated correlation sequence storage system 420 in anaddressable memory 430 of the remote processing system 2000 for re-use.

In some but not necessarily all examples, the correlation result 312 isreturned to the remote device 1000 via the communications link(s) 1500.

In some but not necessarily all examples, the phase-compensatedcorrelation sequence 322 is returned to the remote device 1000 via thecommunications link(s) 1500.

In some but not necessarily all examples, the controller 800 performsadditional post-processing of the correlation results 312 to derivehigher-value outputs 801 (e.g. GNSS pseudoranges or position fixes fromGNSS signals) that are transferred to the remote device 1000 viacommunications link(s) 1500.

FIG. 14B illustrates another example of a system comprising a remotedevice 1000 and a remote processing system 2000. The remote device 1000comprises the receiver 200 and the phase parameter module 360. The phaseparameter module 360 provides the parameter information 361 to theremote processing system 2000. In this example, the phase parametermodule 360 is a receiver-motion module 360 comprising receiver-motionsensors that provide receiver-motion sensor data (movement signals) asthe parameter information 361. The remote device 1000 is physicallydistant from the remote processing system 2000 comprising the controller800. The remote device 1000 and the remote processing system 2000communicate via communications link(s) 1500. The communications link(s)1500 may comprise of, for example, wireless communications (e.g. WiFi,BLE, Cellular Telephony, Satellite comms), cabled communications (e.g.Ethernet, landline telephone, fibre optic cable), physical storage mediathat may be transported between components (e.g. solid state memory,CD-ROM) or any combination thereof.

The receiver-motion sensor data is provided as parameter information 361by the remote device 1000 to the remote processing system 2000 via thecommunications link(s) 1500.

Part of the phase-compensated correlator 300 (correlator 310) is in theremote device 1000 and part (phase-compensated correlation sequencegenerator 320) is in the remote processing system 2000.

The phase-compensated correlation sequence generator 320 in the remoteprocessing system 2000 generates a phase-compensated correlationsequence 322 from processing of the received parameter information 361.The phase-compensated correlation sequence 322 is transferred from theremote processing system 2000 to the remote device 100 via thecommunications link(s) 1500.

The digital signal 222 is not provided by the remote device 1000 to theremote processing system 2000 via the communications link(s) 1500.Instead it is provided to the correlator 310 in the remote device 1000.The correlator 310 performs phase-compensated correlation of the digitalsignal 222 using the transferred phase-compensated correlation sequence322 to produce correlation result 312.

At the remote device 1000, the phase-compensated correlation sequence322 may optionally be stored by a phase-compensated correlation sequencestorage system 420 in an addressable memory 430 of the remote device1000 for re-use.

In a variation of the above described examples, the receiver-motionmodule 360 may be configured to process the receiver-motion sensor datato derive a measured or assumed receiver-motion value that is providedas parameter information 361. This processed parameter information 361may be passed to the remote processing system 2000 instead of the rawreceiver-motion sensor data, removing the need for the remote processingsystem 2000 to calculate the receiver-motion from the receiver-motionsensors data.

In a variation of the above described examples, the receiver-motionmodule 360 may not be located at the remote device 1000, but may belocated elsewhere, for example, at the remote processing system 2000 orelsewhere.

FIG. 14C illustrates another example of a system comprising a remotedevice 1000 and a remote processing system 2000. This system is similarto that illustrated in FIG. 14A, however, the correlation results 312(and/or higher value outputs 801) are not provided to the remote device1000. The correlation results 312 (and/or higher value outputs 801) areutilised/stored at the remote processing system 2000, or are provided toremote third-party clients 3000 via communications link(s) 2500 forfurther use/processing/storage.

It should be understood that the above examples may be further modifiedto include a plurality of remote devices 1000, and/or a plurality ofremote processing systems 2000 and/or a plurality of remote third partyclients 3000, all connected by a plurality of communications links1500/2500.

The receiver 200 and the phase-compensated correlator 300 previouslydescribed and illustrated may, for example, be used for GNSS systems,radio systems (e.g. OFDM, DVB-T, LTE), sonar systems, laser systems,seismic systems etc.

The term ‘causing or performing’ as it appears in the claims may mean tocause but not perform, to perform but not cause or to cause and perform.If an entity causes an action it means removal of the entity would meanthat the action does not occur. If an entity performs an action theentity carries out the action.

The interconnection of items in a Figure indicates operational couplingand any number or combination of intervening elements can exist(including no intervening elements).

Where a structural feature has been described, it may be replaced bymeans for performing one or more of the functions of the structuralfeature whether that function or those functions are explicitly orimplicitly described.

As used here ‘hardware module’ refers to a physical unit or apparatusthat excludes certain parts/components that would be added by an endmanufacturer or a user. A phase-compensated correlator 300 may be ahardware module. A phase-compensated correlation sequence generator 320may be or may be part of a hardware module. A phase-compensated phasorgenerator 330 may be or may be part of a hardware module. A correlationcode generator 340 may be or may be part of a hardware module. A phaseparameter module 360, for example a receiver-motion module 360 may be ormay be part of a hardware module. A correlator 310 may be or may be partof a hardware module. A phase-compensated correlation sequence storagesystem may be or may be part of a hardware module.

The term ‘comprise’ is used in this document with an inclusive not anexclusive meaning. That is any reference to X comprising Y indicatesthat X may comprise only one Y or may comprise more than one Y. If it isintended to use ‘comprise’ with an exclusive meaning then it will bemade clear in the context by referring to “comprising only one . . . ”or by using “consisting”.

In this brief description, reference has been made to various examples.The description of features or functions in relation to an exampleindicates that those features or functions are present in that example.The use of the term ‘example’ or ‘for example’ or ‘may’ in the textdenotes, whether explicitly stated or not, that such features orfunctions are present in at least the described example, whetherdescribed as an example or not, and that they can be, but are notnecessarily, present in some of or all other examples. Thus ‘example’,‘for example’ or ‘may’ refers to a particular instance in a class ofexamples. A property of the instance can be a property of only thatinstance or a property of the class or a property of a sub-class of theclass that includes some but not all of the instances in the class. Itis therefore implicitly disclosed that a features described withreference to one example but not with reference to another example, canwhere possible be used in that other example but does not necessarilyhave to be used in that other example.

Although embodiments of the present invention have been described in thepreceding paragraphs with reference to various examples, it should beappreciated that modifications to the examples given can be made withoutdeparting from the scope of the invention as claimed.

It may be desirable to remove data modulation from the signal (called“data wipe-off” in GNSS terms), which, for example for abinary-phase-shift-keying (BPSK) modulation is done by applying a +/−πphase shift for each sample. The term phase compensation implies thatthe compensated phase can be one of multiple values not limited to +/−π.The absence (or presence) of phase compensation does not thereforeprevent data wipe-off.

It may be desirable to use more than one correlator for correlation ofconcatenated correlation code words. It is important that phasecoherency is maintained between correlators such that the start phase ofa correlator corresponds to the end phase of the immediately precedingcorrelator and the end phase of the correlator corresponds to the startphase of the immediately following correlator.

Features described in the preceding description may be used incombinations other than the combinations explicitly described.

Although functions have been described with reference to certainfeatures, those functions may be performable by other features whetherdescribed or not.

Although features have been described with reference to certainembodiments, those features may also be present in other embodimentswhether described or not.

Whilst endeavoring in the foregoing specification to draw attention tothose features of the invention believed to be of particular importanceit should be understood that the Applicant claims protection in respectof any patentable feature or combination of features hereinbeforereferred to and/or shown in the drawings whether or not particularemphasis has been placed thereon.

1.-33. (canceled)
 34. A method for identifying an unauthorized signalusing a signal processing system, comprising: receiving at least onesignal from at least one remote source; determining motion of at least aportion of the signal processing system; correlating at least one localsignal with the at least one received signal to generate at least onecorrelation result; motion compensating the at least one local signal,the at least one received signal or the at least one correlation resultusing the determined motion to produce at least one motion compensatedcorrelation result; compensating a phase evolution of at least one ofthe at least one local signal, the at least one received signal and theat least one motion compensated correlation result based on a pluralityof hypotheses to generate at least one phase-compensated correlationresult; determining a preferred hypothesis in the plurality ofhypotheses that maximizes the at least one phase compensated correlationresult; identifying a direction of arrival for the at least one receivedsignal using the preferred hypothesis; and determining, from thedirection of arrival of at least one received signal, whether the atleast one received signal is an unauthorized signal.
 35. The method ofclaim 34, further comprising rejecting the unauthorized signal.
 36. Themethod of claim 34, wherein identifying the direction of arrival for theat least one received signal as being a line-of-sight direction or anon-line-of-sight direction to the at least one remote source.
 37. Themethod of claim 34, wherein the signal processing system comprises apositioning system and further comprising computing a position of thepositioning system using the at least one received signal that isauthorized and not using the unauthorized signal.
 38. The method ofclaim 34, wherein the unauthorized signal arrives at the signalprocessing system from an unexpected direction.
 39. The method of claim34, wherein identifying the direction of arrival for the at least onereceived signal as being an expected direction or an unexpecteddirection to the at least one remote source.
 40. The method of claim 34,further comprising constraining the direction of arrival of the at leastone received signal to a range and only using the at least one receivedsignal having a direction of arrival within the range.
 41. The method ofclaim 34, wherein the at least one received signal comprises a pluralityof received signals and the method further comprises: identifying adirection of arrival for each received signal of the plurality ofreceived signals using the preferred hypothesis; and determining, fromthe direction of arrival of each received signal, whether any of theplurality of received signals are unauthorized signals.
 42. Apparatusfor identifying an unauthorized signal using a signal processing system,comprising at least one processor and at least one non-transientcomputer readable medium for storing instructions that, when executed bythe at least one processor, causes the apparatus to perform operationscomprising: receiving at least one signal from at least one remotesource; determining motion of at least a portion of the signalprocessing system; correlating at least one local signal with the atleast one received signal to generate at least one correlation result;motion compensating the at least one local signal, the at least onereceived signal or the at least one correlation result using thedetermined motion to produce at least one motion compensated correlationresult; compensating a phase evolution of at least one of the at leastone local signal, the at least one received signal and the at least onemotion compensated correlation result based on a plurality of hypothesesto generate at least one phase-compensated correlation result;determining a preferred hypothesis in the plurality of hypotheses thatmaximizes the at least one phase compensated correlation result;identifying a direction of arrival for the at least one received signalusing the preferred hypothesis; and determining, from the direction ofarrival of at least one received signal, whether the at least onereceived signal is an unauthorized signal.
 43. The apparatus of claim42, further comprising rejecting the unauthorized signal.
 44. Theapparatus of claim 42, wherein identifying the direction of arrival forthe at least one received signal as being a line-of-sight direction or anon-line-of-sight direction to the at least one remote source.
 45. Theapparatus of claim 42, wherein the signal processing system comprises apositioning system and further comprising computing a position of thepositioning system using the at least one received signal that isauthorized and not using the unauthorized signal.
 46. The apparatus ofclaim 42, wherein the unauthorized signal arrives from an unexpecteddirection.
 47. The apparatus of claim 42, wherein identifying thedirection of arrival for the at least one received signal as being anexpected direction or an unexpected direction to the at least one remotesource.
 48. The apparatus of claim 42, further comprising constrainingthe direction of arrival of the at least one received signals to a rangeand only using the at least one received signal having a direction ofarrival within the range.
 49. The apparatus of claim 42, wherein the atleast one received signal comprises a plurality of received signals andthe operations further comprise: identifying a direction of arrival foreach received signal of the plurality of received signals using thepreferred hypothesis; and determining, from the direction of arrival ofeach received signal, whether any of the plurality of received signalsare unauthorized signals.
 50. A method for identifying an unauthorizedsignal using a signal processing system, comprising: receiving aplurality of signals from a plurality of remote sources; determiningmotion of at least a portion of the signal processing system;correlating a locals signal with each received signal in the pluralityof received signal to generate a plurality of correlation results;motion compensating the local signal, the plurality of received signalsor the plurality of correlation results using the determined motion toproduce a plurality of motion compensated correlation results;compensating a phase evolution of at least one of the local signal, theplurality of received signals and the plurality of motion compensatedcorrelation results based on a plurality of hypotheses to generate aplurality of phase-compensated correlation results; determining apreferred hypothesis in the plurality of hypotheses that maximizes aphase compensated correlation result in the plurality of phasecompensated correlation results; identifying a direction of arrival foreach received signal in the plurality of received signals using thepreferred hypothesis; and determining, from the direction of arrival ofat least one received signal, whether the at least one received signalis an unauthorized signal.
 51. The method of claim 50, wherein thesignal processing system is a positioning system.
 52. The method ofclaim 51, further comprising rejecting the unauthorized signal from usein determining a position of the positioning system.
 53. The method ofclaim 50, wherein identifying the direction of arrival for each receivedsignal as being a line-of-sight direction or a non-line-of-sightdirection to each remote source.